Migrate Apigee system to AWS API Gateway

One of the first steps is to do an Open API export of the APIs. (API Gateway supports OpenAPI 3) Then import it to AWS through console. Check for errors and fix them as you go along. Understand that there will be nuances in the way the code is written in the one platform and refactor/fix bugs as you complete migration. AWS documentation is extensive and checkout the developer guide.
https://docs.aws.amazon.com/apigateway/index.html

The above is one example of how the migration could be done but depending on your customer need, there may be other approaches that could be pursued.

Here is a case study on how a customer migrated to API Gateway. [https://aws.amazon.com/blogs/mt/migrating-to-amazon-apigateway-datalex/]