api gateway invoke lambda cloudformation

Please refer AWS Resource API Gateway Method documentation for examples.

Cloudformation template should look like somethings as below, it may require additional tweaks based on your use cace exactly:

    apiGatewayMethod:
    Type: AWS::ApiGateway::Method
    Properties:
        AuthorizationType: NONE
        HttpMethod: !Ref apiGatewayHTTPMethod
        Integration:
        IntegrationHttpMethod: POST
        Type: AWS_PROXY
        Uri: !Sub
            - arn:aws:apigateway:${AWS::Region}:lambda:path/.../functions/${lambdaArn}/invocations
            - lambdaArn: !GetAtt lambdaFunction.Arn
        ResourceId: !GetAtt apiGateway.RootResourceId
        RestApiId: !Ref apiGateway

    lambdaApiGatewayInvoke:
        Type: AWS::Lambda::Permission
        Properties:
        Action: lambda:InvokeFunction
        FunctionName: !GetAtt lambdaFunction.Arn
        Principal: apigateway.amazonaws.com
        SourceArn: !Sub arn:aws:execute-api:${AWS::Region}:${AWS::AccountId}:${apiGateway}/<APIGatewayStageName>/<apiGatewayHTTPMethod>/

Hope you find this useful.

Comment here if you have additional questions, happy to help.

Abhishek