The 17-year-old free agent, who last played for non-league Hemel Hempstead, has been training with Marc Bircham's development squad over the last few weeks.
Bircham told the club's official website: "Ben has done really well since coming in, he's played a couple of games for us and applied himself well in training.
"I'm pleased we've managed to get him in. There were a lot of clubs interested and he's chosen QPR which is always flattering for us.
"He's still a young lad, he still qualifies for the youth team where he'll be playing for the next few games, and hopefully he'll score goals and come and play in the elite development squad when needed. Hopefully we can make him a better player."