How can I automatically give permission to the API Gateway to use a Lambda function?

I have written the swagger definition and I have successfully integrated API Gateway and Lambda function. When I am trying to use the endpoint though I am receiving an execution role. 

API Gateway does not have permission to assume the provided role 

  In order to fix that, I have to manually go to Integration request, edit the region and re-enter the lambda function name in order to give permissions. Is there any work around to automate that process?

Kind regards,

Giorgos Ioannidis