How to enable Cloudwatch logging for AWS API GW via Cloudformation template

Please add MetricsEnabled property in StageDescription to enabled CloudWatch log at stage level. If you want to enable CloudWatch logs at the method level, add MetricsEnabled property in MethodSettigns. In the following example, I have enabled logs in both places.

TestDeployment:
  Type: AWS::ApiGateway::Deployment
  Properties:
    Description: API Deployment
    RestApiId: testApi
    StageName: 'dev'
    StageDescription:
      Description: Stage - DEV
      LoggingLevel: INFO
      MetricsEnabled: True
      MethodSettings:
        - ResourcePath: "/testresource"
          HttpMethod: "POST"
          LoggingLevel: INFO
          MetricsEnabled: True

UPDATE For APIGatewayV2 - Access Logs only (Execution logs aren't available for http).

The AWS documentation is pretty unclear. After some days of shotgun programming, I found this. Here is a Cloudformation with API Gateway v2 that worked for me:

MyLogGroup:
    Type: AWS::Logs::LogGroup
    Properties:
      LogGroupName: /aws/apigateway/nameOfLogGroupForCloudWatch
      RetentionInDays: 7
MyStage:
    Type: AWS::ApiGatewayV2::Stage
    Properties:
      # Begin CloudWatch
      AccessLogSettings:
        DestinationArn: !GetAtt MyLogGroup.Arn # This points to the log group above
        Format: '{ "requestId": "$context.requestId", "path": "$context.path", "routeKey": "$context.routeKey", "ip": "$context.identity.sourceIp", "requestTime": "$context.requestTime", "httpMethod": "$context.httpMethod","statusCode": $context.status }'

Have you already configure API Gateway RestApi to write logs into CloudWatch as describe in AWS documentation : https://docs.aws.amazon.com/apigateway/latest/developerguide/set-up-logging.html

Note that you must set permissions for CloudWatch logging.