diff --git a/src/material-experimental/mdc-select/select.spec.ts b/src/material-experimental/mdc-select/select.spec.ts
index 246493586229..f921749377da 100644
--- a/src/material-experimental/mdc-select/select.spec.ts
+++ b/src/material-experimental/mdc-select/select.spec.ts
@@ -222,6 +222,22 @@ describe('MDC-based MatSelect', () => {
           expect(select.getAttribute('tabindex')).toEqual('0');
         }));
 
+        it('should set `aria-describedby` to the id of the mat-hint', fakeAsync(() => {
+          expect(select.getAttribute('aria-describedby')).toBeNull();
+
+          fixture.componentInstance.hint = 'test';
+          fixture.detectChanges();
+          const hint = fixture.debugElement.query(By.css('mat-hint')).nativeElement;
+          expect(select.getAttribute('aria-describedby')).toBe(hint.getAttribute('id'));
+          expect(select.getAttribute('aria-describedby')).toMatch(/^mat-mdc-hint-\d+$/);
+        }));
+
+        it('should support user binding to `aria-describedby`', fakeAsync(() => {
+          fixture.componentInstance.ariaDescribedBy = 'test';
+          fixture.detectChanges();
+          expect(select.getAttribute('aria-describedby')).toBe('test');
+        }));
+
         it('should be able to override the tabindex', fakeAsync(() => {
           fixture.componentInstance.tabIndexOverride = 3;
           fixture.detectChanges();
@@ -4223,13 +4239,15 @@ describe('MDC-based MatSelect', () => {
     <mat-form-field>
       <mat-label *ngIf="hasLabel">Select a food</mat-label>
       <mat-select placeholder="Food" [formControl]="control" [required]="isRequired"
-        [tabIndex]="tabIndexOverride" [aria-label]="ariaLabel" [aria-labelledby]="ariaLabelledby"
+        [tabIndex]="tabIndexOverride" [aria-describedby]="ariaDescribedBy"
+        [aria-label]="ariaLabel" [aria-labelledby]="ariaLabelledby"
         [panelClass]="panelClass" [disableRipple]="disableRipple"
         [typeaheadDebounceInterval]="typeaheadDebounceInterval">
         <mat-option *ngFor="let food of foods" [value]="food.value" [disabled]="food.disabled">
           {{ food.viewValue }}
         </mat-option>
       </mat-select>
+      <mat-hint *ngIf="hint">{{ hint }}</mat-hint>
     </mat-form-field>
     <div [style.height.px]="heightBelow"></div>
   `,
@@ -4250,7 +4268,9 @@ class BasicSelect {
   heightAbove = 0;
   heightBelow = 0;
   hasLabel = true;
+  hint: string;
   tabIndexOverride: number;
+  ariaDescribedBy: string;
   ariaLabel: string;
   ariaLabelledby: string;
   panelClass = ['custom-one', 'custom-two'];
diff --git a/src/material-experimental/mdc-select/select.ts b/src/material-experimental/mdc-select/select.ts
index 0c67c796cd05..2256f06c9bee 100644
--- a/src/material-experimental/mdc-select/select.ts
+++ b/src/material-experimental/mdc-select/select.ts
@@ -72,7 +72,6 @@ export class MatSelectTrigger {}
     '[attr.aria-required]': 'required.toString()',
     '[attr.aria-disabled]': 'disabled.toString()',
     '[attr.aria-invalid]': 'errorState',
-    '[attr.aria-describedby]': '_ariaDescribedby || null',
     '[attr.aria-activedescendant]': '_getAriaActiveDescendant()',
     '[class.mat-mdc-select-disabled]': 'disabled',
     '[class.mat-mdc-select-invalid]': 'errorState',
diff --git a/src/material/select/select.spec.ts b/src/material/select/select.spec.ts
index 11c25bebadd9..d393c2a9933d 100644
--- a/src/material/select/select.spec.ts
+++ b/src/material/select/select.spec.ts
@@ -298,6 +298,22 @@ describe('MatSelect', () => {
           expect(select.getAttribute('aria-labelledby')?.trim()).toBe(valueId);
         });
 
+        it('should set `aria-describedby` to the id of the mat-hint', fakeAsync(() => {
+          expect(select.getAttribute('aria-describedby')).toBeNull();
+
+          fixture.componentInstance.hint = 'test';
+          fixture.detectChanges();
+          const hint = fixture.debugElement.query(By.css('.mat-hint')).nativeElement;
+          expect(select.getAttribute('aria-describedby')).toBe(hint.getAttribute('id'));
+          expect(select.getAttribute('aria-describedby')).toMatch(/^mat-hint-\d+$/);
+        }));
+
+        it('should support user binding to `aria-describedby`', fakeAsync(() => {
+          fixture.componentInstance.ariaDescribedBy = 'test';
+          fixture.detectChanges();
+          expect(select.getAttribute('aria-describedby')).toBe('test');
+        }));
+
         it('should select options via the UP/DOWN arrow keys on a closed select', fakeAsync(() => {
           const formControl = fixture.componentInstance.control;
           const options = fixture.componentInstance.options.toArray();
@@ -5186,13 +5202,15 @@ describe('MatSelect', () => {
     <div [style.height.px]="heightAbove"></div>
     <mat-form-field>
       <mat-select placeholder="Food" [formControl]="control" [required]="isRequired"
-        [tabIndex]="tabIndexOverride" [aria-label]="ariaLabel" [aria-labelledby]="ariaLabelledby"
+        [tabIndex]="tabIndexOverride" [aria-describedby]="ariaDescribedBy"
+        [aria-label]="ariaLabel" [aria-labelledby]="ariaLabelledby"
         [panelClass]="panelClass" [disableRipple]="disableRipple"
         [typeaheadDebounceInterval]="typeaheadDebounceInterval">
         <mat-option *ngFor="let food of foods" [value]="food.value" [disabled]="food.disabled">
           {{ food.viewValue }}
         </mat-option>
       </mat-select>
+      <mat-hint *ngIf="hint">{{ hint }}</mat-hint>
     </mat-form-field>
     <div [style.height.px]="heightBelow"></div>
   `,
@@ -5212,7 +5230,9 @@ class BasicSelect {
   isRequired: boolean;
   heightAbove = 0;
   heightBelow = 0;
+  hint: string;
   tabIndexOverride: number;
+  ariaDescribedBy: string;
   ariaLabel: string;
   ariaLabelledby: string;
   panelClass = ['custom-one', 'custom-two'];
diff --git a/src/material/select/select.ts b/src/material/select/select.ts
index fd0241d767d6..6ff99d1b019a 100644
--- a/src/material/select/select.ts
+++ b/src/material/select/select.ts
@@ -303,8 +303,11 @@ export abstract class _MatSelectBase<C>
   /** Emits whenever the component is destroyed. */
   protected readonly _destroy = new Subject<void>();
 
-  /** The aria-describedby attribute on the select for improved a11y. */
-  _ariaDescribedby: string;
+  /**
+   * Implemented as part of MatFormFieldControl.
+   * @docs-private
+   */
+  @Input('aria-describedby') userAriaDescribedBy: string;
 
   /** Deals with the selection logic. */
   _selectionModel: SelectionModel<MatOption>;
@@ -611,7 +614,7 @@ export abstract class _MatSelectBase<C>
   ngOnChanges(changes: SimpleChanges) {
     // Updating the disabled state is handled by `mixinDisabled`, but we need to additionally let
     // the parent form field know to run change detection when the disabled state changes.
-    if (changes['disabled']) {
+    if (changes['disabled'] || changes['userAriaDescribedBy']) {
       this.stateChanges.next();
     }
 
@@ -1146,7 +1149,11 @@ export abstract class _MatSelectBase<C>
    * @docs-private
    */
   setDescribedByIds(ids: string[]) {
-    this._ariaDescribedby = ids.join(' ');
+    if (ids.length) {
+      this._elementRef.nativeElement.setAttribute('aria-describedby', ids.join(' '));
+    } else {
+      this._elementRef.nativeElement.removeAttribute('aria-describedby');
+    }
   }
 
   /**
@@ -1191,7 +1198,6 @@ export abstract class _MatSelectBase<C>
     '[attr.aria-required]': 'required.toString()',
     '[attr.aria-disabled]': 'disabled.toString()',
     '[attr.aria-invalid]': 'errorState',
-    '[attr.aria-describedby]': '_ariaDescribedby || null',
     '[attr.aria-activedescendant]': '_getAriaActiveDescendant()',
     '[class.mat-select-disabled]': 'disabled',
     '[class.mat-select-invalid]': 'errorState',
diff --git a/tools/public_api_guard/material/select.md b/tools/public_api_guard/material/select.md
index a21247cc2fc1..d9c0cea39ae3 100644
--- a/tools/public_api_guard/material/select.md
+++ b/tools/public_api_guard/material/select.md
@@ -114,7 +114,6 @@ export const matSelectAnimations: {
 // @public
 export abstract class _MatSelectBase<C> extends _MatSelectMixinBase implements AfterContentInit, OnChanges, OnDestroy, OnInit, DoCheck, ControlValueAccessor, CanDisable, HasTabIndex, MatFormFieldControl<any>, CanUpdateErrorState, CanDisableRipple {
     constructor(_viewportRuler: ViewportRuler, _changeDetectorRef: ChangeDetectorRef, _ngZone: NgZone, _defaultErrorStateMatcher: ErrorStateMatcher, elementRef: ElementRef, _dir: Directionality, _parentForm: NgForm, _parentFormGroup: FormGroupDirective, _parentFormField: MatFormField, ngControl: NgControl, tabIndex: string, scrollStrategyFactory: any, _liveAnnouncer: LiveAnnouncer, _defaultOptions?: MatSelectConfig | undefined);
-    _ariaDescribedby: string;
     ariaLabel: string;
     ariaLabelledby: string;
     protected _canOpen(): boolean;
@@ -203,6 +202,7 @@ export abstract class _MatSelectBase<C> extends _MatSelectMixinBase implements A
     get triggerValue(): string;
     get typeaheadDebounceInterval(): number;
     set typeaheadDebounceInterval(value: NumberInput);
+    userAriaDescribedBy: string;
     get value(): any;
     set value(newValue: any);
     readonly valueChange: EventEmitter<any>;
@@ -211,7 +211,7 @@ export abstract class _MatSelectBase<C> extends _MatSelectMixinBase implements A
     protected _viewportRuler: ViewportRuler;
     writeValue(value: any): void;
     // (undocumented)
-    static ɵdir: i0.ɵɵDirectiveDeclaration<_MatSelectBase<any>, never, never, { "panelClass": "panelClass"; "placeholder": "placeholder"; "required": "required"; "multiple": "multiple"; "disableOptionCentering": "disableOptionCentering"; "compareWith": "compareWith"; "value": "value"; "ariaLabel": "aria-label"; "ariaLabelledby": "aria-labelledby"; "errorStateMatcher": "errorStateMatcher"; "typeaheadDebounceInterval": "typeaheadDebounceInterval"; "sortComparator": "sortComparator"; "id": "id"; }, { "openedChange": "openedChange"; "_openedStream": "opened"; "_closedStream": "closed"; "selectionChange": "selectionChange"; "valueChange": "valueChange"; }, never>;
+    static ɵdir: i0.ɵɵDirectiveDeclaration<_MatSelectBase<any>, never, never, { "userAriaDescribedBy": "aria-describedby"; "panelClass": "panelClass"; "placeholder": "placeholder"; "required": "required"; "multiple": "multiple"; "disableOptionCentering": "disableOptionCentering"; "compareWith": "compareWith"; "value": "value"; "ariaLabel": "aria-label"; "ariaLabelledby": "aria-labelledby"; "errorStateMatcher": "errorStateMatcher"; "typeaheadDebounceInterval": "typeaheadDebounceInterval"; "sortComparator": "sortComparator"; "id": "id"; }, { "openedChange": "openedChange"; "_openedStream": "opened"; "_closedStream": "closed"; "selectionChange": "selectionChange"; "valueChange": "valueChange"; }, never>;
     // (undocumented)
     static ɵfac: i0.ɵɵFactoryDeclaration<_MatSelectBase<any>, [null, null, null, null, null, { optional: true; }, { optional: true; }, { optional: true; }, { optional: true; }, { optional: true; self: true; }, { attribute: "tabindex"; }, null, null, { optional: true; }]>;
 }