I ran across this looking for the same thing. The accepted answer works, but I noticed some comments about not being batchable. I found an option for batching and I thought I'd share.
You can use the /upgrade option in devenv.com. This means it's batchable. For example, to recurse the current directory upgrading all .sln files (after backing them up), you could do this:
The other solutions here didn't work for me. My project was created in Visual Studio 2012, and I am now using Visual Studio 2015, but this should work if you're going from 2013 to 2015. This is how you manually upgrade a project from a earlier version to a newer one: