You can use TFS builds to trigger release in VS Release Management. I have encountered some issues while testing this and thought worth sharing for the benefit of the others facing the same.
Issue 1 - The directory name is invalid
How to resolve?
Install the VS Release Management Client in the build server and connect it to Release management server. The connecting user does not matter here.
Issue 2 - Release build failed
How to solve?
As you can see in the image it says TFS Build service account needs to be added to Release Management server as a system user.
Release can be now triggered from TFS build and succeeds.