diff --git a/src/material/button-toggle/button-toggle.html b/src/material/button-toggle/button-toggle.html
index 0a1b9a06eeaf..dc70074e886c 100644
--- a/src/material/button-toggle/button-toggle.html
+++ b/src/material/button-toggle/button-toggle.html
@@ -1,8 +1,10 @@
 <button #button class="mat-button-toggle-button mat-focus-indicator"
         type="button"
         [id]="buttonId"
+        [attr.role]="isSingleSelector() ? 'radio' : 'button'"
         [attr.tabindex]="disabled ? -1 : tabIndex"
-        [attr.aria-pressed]="checked"
+        [attr.aria-pressed]="!isSingleSelector() ? checked : null"
+        [attr.aria-checked]="isSingleSelector() ? checked : null"
         [disabled]="disabled || null"
         [attr.name]="_getButtonName()"
         [attr.aria-label]="ariaLabel"
diff --git a/src/material/button-toggle/button-toggle.spec.ts b/src/material/button-toggle/button-toggle.spec.ts
index 20265dd178fa..c6c4952d16eb 100644
--- a/src/material/button-toggle/button-toggle.spec.ts
+++ b/src/material/button-toggle/button-toggle.spec.ts
@@ -366,6 +366,24 @@ describe('MatButtonToggle without forms', () => {
       buttonToggleInstances = buttonToggleDebugElements.map(debugEl => debugEl.componentInstance);
     });
 
+    it('should initialize the tab index correctly', () => {
+      buttonToggleLabelElements.forEach((buttonToggle, index) => {
+        if (index === 0) {
+          expect(buttonToggle.getAttribute('tabindex')).toBe('0');
+        } else {
+          expect(buttonToggle.getAttribute('tabindex')).toBe('-1');
+        }
+      });
+    });
+
+    it('should update the tab index correctly', () => {
+      buttonToggleLabelElements[1].click();
+      fixture.detectChanges();
+
+      expect(buttonToggleLabelElements[0].getAttribute('tabindex')).toBe('-1');
+      expect(buttonToggleLabelElements[1].getAttribute('tabindex')).toBe('0');
+    });
+
     it('should set individual button toggle names based on the group name', () => {
       expect(groupInstance.name).toBeTruthy();
       for (let buttonToggle of buttonToggleLabelElements) {
diff --git a/src/material/button-toggle/button-toggle.ts b/src/material/button-toggle/button-toggle.ts
index ab9c8a527928..42c0d7175264 100644
--- a/src/material/button-toggle/button-toggle.ts
+++ b/src/material/button-toggle/button-toggle.ts
@@ -8,6 +8,7 @@
 
 import {FocusMonitor} from '@angular/cdk/a11y';
 import {SelectionModel} from '@angular/cdk/collections';
+import {DOWN_ARROW, LEFT_ARROW, RIGHT_ARROW, UP_ARROW, SPACE, ENTER} from '@angular/cdk/keycodes';
 import {
   AfterContentInit,
   Attribute,
@@ -32,6 +33,7 @@ import {
   AfterViewInit,
   booleanAttribute,
 } from '@angular/core';
+import {Direction, Directionality} from '@angular/cdk/bidi';
 import {ControlValueAccessor, NG_VALUE_ACCESSOR} from '@angular/forms';
 import {MatRipple, MatPseudoCheckbox} from '@angular/material/core';
 
@@ -121,8 +123,9 @@ export class MatButtonToggleChange {
     {provide: MAT_BUTTON_TOGGLE_GROUP, useExisting: MatButtonToggleGroup},
   ],
   host: {
-    'role': 'group',
     'class': 'mat-button-toggle-group',
+    '(keydown)': '_keydown($event)',
+    '[attr.role]': "multiple ? 'group' : 'radiogroup'",
     '[attr.aria-disabled]': 'disabled',
     '[class.mat-button-toggle-vertical]': 'vertical',
     '[class.mat-button-toggle-group-appearance-standard]': 'appearance === "standard"',
@@ -226,6 +229,11 @@ export class MatButtonToggleGroup implements ControlValueAccessor, OnInit, After
     this._markButtonsForCheck();
   }
 
+  /** The layout direction of the toggle button group. */
+  get dir(): Direction {
+    return this._dir && this._dir.value === 'rtl' ? 'rtl' : 'ltr';
+  }
+
   /** Event emitted when the group's value changes. */
   @Output() readonly change: EventEmitter<MatButtonToggleChange> =
     new EventEmitter<MatButtonToggleChange>();
@@ -257,6 +265,7 @@ export class MatButtonToggleGroup implements ControlValueAccessor, OnInit, After
     @Optional()
     @Inject(MAT_BUTTON_TOGGLE_DEFAULT_OPTIONS)
     defaultOptions?: MatButtonToggleDefaultOptions,
+    @Optional() private _dir?: Directionality,
   ) {
     this.appearance =
       defaultOptions && defaultOptions.appearance ? defaultOptions.appearance : 'standard';
@@ -270,6 +279,9 @@ export class MatButtonToggleGroup implements ControlValueAccessor, OnInit, After
 
   ngAfterContentInit() {
     this._selectionModel.select(...this._buttonToggles.filter(toggle => toggle.checked));
+    if (!this.multiple) {
+      this._initializeTabIndex();
+    }
   }
 
   /**
@@ -296,6 +308,49 @@ export class MatButtonToggleGroup implements ControlValueAccessor, OnInit, After
     this.disabled = isDisabled;
   }
 
+  /** Handle keydown event calling to single-select button toggle. */
+  protected _keydown(event: KeyboardEvent) {
+    if (this.multiple || this.disabled) {
+      return;
+    }
+
+    const target = event.target as HTMLButtonElement;
+    const buttonId = target.id;
+    const index = this._buttonToggles.toArray().findIndex(toggle => {
+      return toggle.buttonId === buttonId;
+    });
+
+    let nextButton;
+    switch (event.keyCode) {
+      case SPACE:
+      case ENTER:
+        nextButton = this._buttonToggles.get(index);
+        break;
+      case UP_ARROW:
+        nextButton = this._buttonToggles.get(this._getNextIndex(index, -1));
+        break;
+      case LEFT_ARROW:
+        nextButton = this._buttonToggles.get(
+          this._getNextIndex(index, this.dir === 'ltr' ? -1 : 1),
+        );
+        break;
+      case DOWN_ARROW:
+        nextButton = this._buttonToggles.get(this._getNextIndex(index, 1));
+        break;
+      case RIGHT_ARROW:
+        nextButton = this._buttonToggles.get(
+          this._getNextIndex(index, this.dir === 'ltr' ? 1 : -1),
+        );
+        break;
+      default:
+        return;
+    }
+
+    event.preventDefault();
+    nextButton?._onButtonClick();
+    nextButton?.focus();
+  }
+
   /** Dispatch change event with current selection and group value. */
   _emitChangeEvent(toggle: MatButtonToggle): void {
     const event = new MatButtonToggleChange(toggle, this.value);
@@ -361,6 +416,31 @@ export class MatButtonToggleGroup implements ControlValueAccessor, OnInit, After
     return toggle.value === this._rawValue;
   }
 
+  /** Initializes the tabindex attribute using the radio pattern. */
+  private _initializeTabIndex() {
+    this._buttonToggles.forEach(toggle => {
+      toggle.tabIndex = -1;
+    });
+    if (this.selected) {
+      (this.selected as MatButtonToggle).tabIndex = 0;
+    } else if (this._buttonToggles.length > 0) {
+      this._buttonToggles.get(0)!.tabIndex = 0;
+    }
+    this._markButtonsForCheck();
+  }
+
+  /** Obtain the subsequent index to which the focus shifts. */
+  private _getNextIndex(index: number, offset: number): number {
+    let nextIndex = index + offset;
+    if (nextIndex === this._buttonToggles.length) {
+      nextIndex = 0;
+    }
+    if (nextIndex === -1) {
+      nextIndex = this._buttonToggles.length - 1;
+    }
+    return nextIndex;
+  }
+
   /** Updates the selection state of the toggles in the group based on a value. */
   private _setSelectionByValue(value: any | any[]) {
     this._rawValue = value;
@@ -385,7 +465,13 @@ export class MatButtonToggleGroup implements ControlValueAccessor, OnInit, After
   /** Clears the selected toggles. */
   private _clearSelection() {
     this._selectionModel.clear();
-    this._buttonToggles.forEach(toggle => (toggle.checked = false));
+    this._buttonToggles.forEach(toggle => {
+      toggle.checked = false;
+      // If the button toggle is in single select mode, initialize the tabIndex.
+      if (!this.multiple) {
+        toggle.tabIndex = -1;
+      }
+    });
   }
 
   /** Selects a value if there's a toggle that corresponds to it. */
@@ -397,6 +483,10 @@ export class MatButtonToggleGroup implements ControlValueAccessor, OnInit, After
     if (correspondingOption) {
       correspondingOption.checked = true;
       this._selectionModel.select(correspondingOption);
+      if (!this.multiple) {
+        // If the button toggle is in single select mode, reset the tabIndex.
+        correspondingOption.tabIndex = 0;
+      }
     }
   }
 
@@ -476,8 +566,16 @@ export class MatButtonToggle implements OnInit, AfterViewInit, OnDestroy {
   /** MatButtonToggleGroup reads this to assign its own value. */
   @Input() value: any;
 
-  /** Tabindex for the toggle. */
-  @Input() tabIndex: number | null;
+  /** Tabindex of the toggle. */
+  @Input()
+  get tabIndex(): number | null {
+    return this._tabIndex;
+  }
+  set tabIndex(value: number | null) {
+    this._tabIndex = value;
+    this._markForCheck();
+  }
+  private _tabIndex: number | null;
 
   /** Whether ripples are disabled on the button toggle. */
   @Input({transform: booleanAttribute}) disableRipple: boolean;
@@ -580,7 +678,7 @@ export class MatButtonToggle implements OnInit, AfterViewInit, OnDestroy {
 
   /** Checks the button toggle due to an interaction with the underlying native button. */
   _onButtonClick() {
-    const newChecked = this._isSingleSelector() ? true : !this._checked;
+    const newChecked = this.isSingleSelector() ? true : !this._checked;
 
     if (newChecked !== this._checked) {
       this._checked = newChecked;
@@ -589,6 +687,19 @@ export class MatButtonToggle implements OnInit, AfterViewInit, OnDestroy {
         this.buttonToggleGroup._onTouched();
       }
     }
+
+    if (this.isSingleSelector()) {
+      const focusable = this.buttonToggleGroup._buttonToggles.find(toggle => {
+        return toggle.tabIndex === 0;
+      });
+      // Modify the tabindex attribute of the last focusable button toggle to -1.
+      if (focusable) {
+        focusable.tabIndex = -1;
+      }
+      // Modify the tabindex attribute of the presently selected button toggle to 0.
+      this.tabIndex = 0;
+    }
+
     // Emit a change event when it's the single selector
     this.change.emit(new MatButtonToggleChange(this, this.value));
   }
@@ -606,14 +717,14 @@ export class MatButtonToggle implements OnInit, AfterViewInit, OnDestroy {
 
   /** Gets the name that should be assigned to the inner DOM node. */
   _getButtonName(): string | null {
-    if (this._isSingleSelector()) {
+    if (this.isSingleSelector()) {
       return this.buttonToggleGroup.name;
     }
     return this.name || null;
   }
 
   /** Whether the toggle is in single selection mode. */
-  private _isSingleSelector(): boolean {
+  isSingleSelector(): boolean {
     return this.buttonToggleGroup && !this.buttonToggleGroup.multiple;
   }
 }
diff --git a/src/material/button-toggle/testing/button-toggle-harness.ts b/src/material/button-toggle/testing/button-toggle-harness.ts
index 5d69fa203381..2063446b4304 100644
--- a/src/material/button-toggle/testing/button-toggle-harness.ts
+++ b/src/material/button-toggle/testing/button-toggle-harness.ts
@@ -6,7 +6,7 @@
  * found in the LICENSE file at https://angular.io/license
  */
 
-import {ComponentHarness, HarnessPredicate} from '@angular/cdk/testing';
+import {ComponentHarness, HarnessPredicate, parallel} from '@angular/cdk/testing';
 import {coerceBooleanProperty} from '@angular/cdk/coercion';
 import {MatButtonToggleAppearance} from '@angular/material/button-toggle';
 import {ButtonToggleHarnessFilters} from './button-toggle-harness-filters';
@@ -45,8 +45,12 @@ export class MatButtonToggleHarness extends ComponentHarness {
 
   /** Gets a boolean promise indicating if the button toggle is checked. */
   async isChecked(): Promise<boolean> {
-    const checked = (await this._button()).getAttribute('aria-pressed');
-    return coerceBooleanProperty(await checked);
+    const button = await this._button();
+    const [checked, pressed] = await parallel(() => [
+      button.getAttribute('aria-checked'),
+      button.getAttribute('aria-pressed'),
+    ]);
+    return coerceBooleanProperty(checked) || coerceBooleanProperty(pressed);
   }
 
   /** Gets a boolean promise indicating if the button toggle is disabled. */
diff --git a/tools/public_api_guard/material/button-toggle.md b/tools/public_api_guard/material/button-toggle.md
index 38d3810694fb..19e7c23ccba0 100644
--- a/tools/public_api_guard/material/button-toggle.md
+++ b/tools/public_api_guard/material/button-toggle.md
@@ -8,6 +8,8 @@ import { AfterContentInit } from '@angular/core';
 import { AfterViewInit } from '@angular/core';
 import { ChangeDetectorRef } from '@angular/core';
 import { ControlValueAccessor } from '@angular/forms';
+import { Direction } from '@angular/cdk/bidi';
+import { Directionality } from '@angular/cdk/bidi';
 import { ElementRef } from '@angular/core';
 import { EventEmitter } from '@angular/core';
 import { FocusMonitor } from '@angular/cdk/a11y';
@@ -49,6 +51,7 @@ export class MatButtonToggle implements OnInit, AfterViewInit, OnDestroy {
     focus(options?: FocusOptions): void;
     _getButtonName(): string | null;
     id: string;
+    isSingleSelector(): boolean;
     _markForCheck(): void;
     name: string;
     // (undocumented)
@@ -64,7 +67,8 @@ export class MatButtonToggle implements OnInit, AfterViewInit, OnDestroy {
     // (undocumented)
     ngOnInit(): void;
     _onButtonClick(): void;
-    tabIndex: number | null;
+    get tabIndex(): number | null;
+    set tabIndex(value: number | null);
     value: any;
     // (undocumented)
     static ɵcmp: i0.ɵɵComponentDeclaration<MatButtonToggle, "mat-button-toggle", ["matButtonToggle"], { "ariaLabel": { "alias": "aria-label"; "required": false; }; "ariaLabelledby": { "alias": "aria-labelledby"; "required": false; }; "id": { "alias": "id"; "required": false; }; "name": { "alias": "name"; "required": false; }; "value": { "alias": "value"; "required": false; }; "tabIndex": { "alias": "tabIndex"; "required": false; }; "disableRipple": { "alias": "disableRipple"; "required": false; }; "appearance": { "alias": "appearance"; "required": false; }; "checked": { "alias": "checked"; "required": false; }; "disabled": { "alias": "disabled"; "required": false; }; }, { "change": "change"; }, never, ["*"], true, never>;
@@ -93,11 +97,12 @@ export interface MatButtonToggleDefaultOptions {
 
 // @public
 export class MatButtonToggleGroup implements ControlValueAccessor, OnInit, AfterContentInit {
-    constructor(_changeDetector: ChangeDetectorRef, defaultOptions?: MatButtonToggleDefaultOptions);
+    constructor(_changeDetector: ChangeDetectorRef, defaultOptions?: MatButtonToggleDefaultOptions, _dir?: Directionality | undefined);
     appearance: MatButtonToggleAppearance;
     _buttonToggles: QueryList<MatButtonToggle>;
     readonly change: EventEmitter<MatButtonToggleChange>;
     _controlValueAccessorChangeFn: (value: any) => void;
+    get dir(): Direction;
     get disabled(): boolean;
     set disabled(value: boolean);
     _emitChangeEvent(toggle: MatButtonToggle): void;
@@ -107,6 +112,7 @@ export class MatButtonToggleGroup implements ControlValueAccessor, OnInit, After
     set hideSingleSelectionIndicator(value: boolean);
     _isPrechecked(toggle: MatButtonToggle): boolean;
     _isSelected(toggle: MatButtonToggle): boolean;
+    protected _keydown(event: KeyboardEvent): void;
     get multiple(): boolean;
     set multiple(value: boolean);
     get name(): string;
@@ -142,7 +148,7 @@ export class MatButtonToggleGroup implements ControlValueAccessor, OnInit, After
     // (undocumented)
     static ɵdir: i0.ɵɵDirectiveDeclaration<MatButtonToggleGroup, "mat-button-toggle-group", ["matButtonToggleGroup"], { "appearance": { "alias": "appearance"; "required": false; }; "name": { "alias": "name"; "required": false; }; "vertical": { "alias": "vertical"; "required": false; }; "value": { "alias": "value"; "required": false; }; "multiple": { "alias": "multiple"; "required": false; }; "disabled": { "alias": "disabled"; "required": false; }; "hideSingleSelectionIndicator": { "alias": "hideSingleSelectionIndicator"; "required": false; }; "hideMultipleSelectionIndicator": { "alias": "hideMultipleSelectionIndicator"; "required": false; }; }, { "valueChange": "valueChange"; "change": "change"; }, ["_buttonToggles"], never, true, never>;
     // (undocumented)
-    static ɵfac: i0.ɵɵFactoryDeclaration<MatButtonToggleGroup, [null, { optional: true; }]>;
+    static ɵfac: i0.ɵɵFactoryDeclaration<MatButtonToggleGroup, [null, { optional: true; }, { optional: true; }]>;
 }
 
 // @public (undocumented)