Hi @pdebruic,
The migration can be finished in a few different ways. I recently finished migration from Eucalyptus to Nutmeg, and everything went smoothly.
Option 1: You can create an AMI and transfer to a new server if your server is hosted by AWS.
Option 2: You can install the same open edx release and then move the database(MySQL + MongoDB) and media assets from the old server to the new server.
Option 3: You can install latest open edX release(Olive) using tutor(version v15.2.0) and then move database(MySQL + MongoDB) and media assets
I followed the following discussion threads and documentation:
How to migrate from a native deployment to a tutor deployment of the Open edX platform
Upgrading koa to nutmeg
These both documents help me a lot in migration. I hope this will help you.