The 20-year-old, who initially joined the League One leaders on a one-month loan deal, has made five appearances this season.
He told Orient's official website: "The strikers here are brilliant and I'm loving learning off them every day. There is a lot to learn from Kevin Lisbie, David Mooney and Shaun Batt, so I have definitely got my notepad out in training.
"There's a great bunch of lads here and I knew a few of them from Bournemouth, which helped me settle in and it has made it a lot easier for me.
"I just want to help the team keep on winning and stay top of the league. I just want to score as many goals as I can to contribute to that and force my way into the manager's plans."
Stockley is currently in his fourth loan spell away from Bournemouth.