Stockley will now remain with the Sky Bet League One leaders until January 4.
The 20-year-old has made five appearances since joining the O's on an initial month-long deal, scoring in a 5-1 win over Notts County last month.
He told Orient's official club website: "The strikers here (at Orient) 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."