diff --git a/packages/aws-cdk-lib/aws-events-targets/lib/log-group.ts b/packages/aws-cdk-lib/aws-events-targets/lib/log-group.ts
index 3f421bc31697d..5ad7c822b28de 100644
--- a/packages/aws-cdk-lib/aws-events-targets/lib/log-group.ts
+++ b/packages/aws-cdk-lib/aws-events-targets/lib/log-group.ts
@@ -1,4 +1,3 @@
-import { LogGroupResourcePolicy } from './log-group-resource-policy';
 import { TargetBaseProps, bindBaseTargetConfig } from './util';
 import * as events from '../../aws-events';
 import { RuleTargetInputProperties, RuleTargetInput, EventField, IRule } from '../../aws-events';
@@ -78,14 +77,6 @@ export interface LogGroupProps extends TargetBaseProps {
    * @default - the entire EventBridge event
    */
   readonly logEvent?: LogGroupTargetInput;
-
-  /**
-   * Whether the custom resource created wll default to
-   * install latest AWS SDK
-   *
-   * @default - install latest AWS SDK
-   */
-  readonly installLatestAwsSdk?: boolean;
 }
 
 /**
@@ -93,15 +84,12 @@ export interface LogGroupProps extends TargetBaseProps {
  */
 export class CloudWatchLogGroup implements events.IRuleTarget {
   private target?: RuleTargetInputProperties;
-  constructor(private readonly logGroup: logs.ILogGroup, private readonly props: LogGroupProps = {}) {}
+  constructor(public readonly logGroup: logs.ILogGroup, private readonly props: LogGroupProps = {}) {}
 
   /**
    * Returns a RuleTarget that can be used to log an event into a CloudWatch LogGroup
    */
   public bind(_rule: events.IRule, _id?: string): events.RuleTargetConfig {
-    // Use a custom resource to set the log group resource policy since it is not supported by CDK and cfn.
-    const resourcePolicyId = `EventsLogGroupPolicy${cdk.Names.nodeUniqueId(_rule.node)}`;
-
     const logGroupStack = cdk.Stack.of(this.logGroup);
 
     if (this.props.event && this.props.logEvent) {
@@ -115,17 +103,7 @@ export class CloudWatchLogGroup implements events.IRuleTarget {
 
     _rule.node.addValidation({ validate: () => this.validateInputTemplate() });
 
-    if (!this.logGroup.node.tryFindChild(resourcePolicyId)) {
-      new LogGroupResourcePolicy(logGroupStack, resourcePolicyId, {
-        installLatestAwsSdk: this.props.installLatestAwsSdk,
-        policyStatements: [new iam.PolicyStatement({
-          effect: iam.Effect.ALLOW,
-          actions: ['logs:PutLogEvents', 'logs:CreateLogStream'],
-          resources: [this.logGroup.logGroupArn],
-          principals: [new iam.ServicePrincipal('events.amazonaws.com')],
-        })],
-      });
-    }
+    this.logGroup.grantWrite(new iam.ServicePrincipal('events.amazonaws.com'));
 
     return {
       ...bindBaseTargetConfig(this.props),
diff --git a/packages/aws-cdk-lib/aws-events-targets/test/logs/log-group.test.ts b/packages/aws-cdk-lib/aws-events-targets/test/logs/log-group.test.ts
index f2670af087148..0f79b2165219e 100644
--- a/packages/aws-cdk-lib/aws-events-targets/test/logs/log-group.test.ts
+++ b/packages/aws-cdk-lib/aws-events-targets/test/logs/log-group.test.ts
@@ -158,46 +158,6 @@ test('logEvent with defaults', () => {
   });
 });
 
-test('can set install latest AWS SDK value to false', () => {
-  // GIVEN
-  const stack = new cdk.Stack();
-  const logGroup = new logs.LogGroup(stack, 'MyLogGroup', {
-    logGroupName: '/aws/events/MyLogGroup',
-  });
-  const rule1 = new events.Rule(stack, 'Rule', {
-    schedule: events.Schedule.rate(cdk.Duration.minutes(1)),
-  });
-
-  // WHEN
-  rule1.addTarget(new targets.CloudWatchLogGroup(logGroup, {
-    installLatestAwsSdk: false,
-  }));
-
-  // THEN
-  Template.fromStack(stack).hasResourceProperties('Custom::CloudwatchLogResourcePolicy', {
-    InstallLatestAwsSdk: false,
-  });
-});
-
-test('default install latest AWS SDK is true', () => {
-  // GIVEN
-  const stack = new cdk.Stack();
-  const logGroup = new logs.LogGroup(stack, 'MyLogGroup', {
-    logGroupName: '/aws/events/MyLogGroup',
-  });
-  const rule1 = new events.Rule(stack, 'Rule', {
-    schedule: events.Schedule.rate(cdk.Duration.minutes(1)),
-  });
-
-  // WHEN
-  rule1.addTarget(new targets.CloudWatchLogGroup(logGroup));
-
-  // THEN
-  Template.fromStack(stack).hasResourceProperties('Custom::CloudwatchLogResourcePolicy', {
-    InstallLatestAwsSdk: true,
-  });
-});
-
 test('can use logEvent', () => {
   // GIVEN
   const stack = new cdk.Stack();
@@ -398,3 +358,31 @@ testDeprecated('specifying retry policy with 0 retryAttempts', () => {
     ],
   });
 });
+
+test('grant write permissions to log group', () => {
+  // GIVEN
+  const stack = new cdk.Stack();
+  const logGroup = new logs.LogGroup(stack, 'MyLogGroup', {
+    logGroupName: '/aws/events/MyLogGroup',
+  });
+  const rule1 = new events.Rule(stack, 'Rule', {
+    schedule: events.Schedule.rate(cdk.Duration.minutes(1)),
+  });
+
+  // WHEN
+  rule1.addTarget(new targets.CloudWatchLogGroup(logGroup));
+
+  // THEN
+  Template.fromStack(stack).hasResourceProperties('AWS::Logs::ResourcePolicy', {
+    PolicyDocument: {
+      Statement: [
+        {
+          Action: ['logs:CreateLogStream', 'logs:PutLogEvents'],
+          Effect: 'Allow',
+          Principal: { Service: 'events.amazonaws.com' },
+          Resource: { 'Fn::GetAtt': ['MyLogGroup5C0DAD85', 'Arn'] },
+        },
+      ],
+    },
+  });
+});
\ No newline at end of file