Stockley made his Cherries debut in 2009 at the age of 16, with the south coast club then playing in the fourth tier, but has been on loan at Sky Bet League Two side Exeter this season.
"We wish him well, he is a player that has been with us a long time and has probably been a victim of our success and the speed of our success," Howe said.
"He is someone who we rated very highly when we were in the League Two days and we believed he had a big future here.
"But the team has moved forward, now we are in the Premier League it becomes more and more difficult for younger players to come through. We wish him well, it is a good move for him at Aberdeen and we hope he goes on to huge success."