My iPhone is connected to iCloud with the same account. In Messages → Preferences, under "You can be reached for Messages at:" my iPhone's number and my iCloud account are both there and checked.
I have tried restarting Messages, my MacBook, as well as turning iMessage off and on from my phone, and removing the files from
~/Library/Messages. Nothing so far has worked.
My computer is running El Capitan, and other applications (such as Notes) can sync over iCloud just fine.