The 19-year-old, who previously spent a loan period at AFC Wimbledon earlier in the season, is regarded as one of the best prospects at the club.
"It is good to get my future sorted. I was always going to sign. I have been on the bench quite a lot this season, which is good," he told the Bees Player.
"Everyone wants to play more but I don't think I would have been offered a contract if the manager didn't trust me and see me as a player for the future. Hopefully that is what he has in store for me."
Reeves will now remain with the club until at least 2015.