The 21-year-old has penned a deal at SN1 until January 2015.
The midfielder is a product of Brentford’s youth system and was on the books at Tottenham Hotspur until the age of 16.
The central midfield player captained the Brentford Youth Team in 2010/11 and made his First Team debut on the final day of that season.
Reeves played 47 games for Brentford in all competitions, scoring one goal.