The striker has been on loan at Exeter since January, but has decided against a permanent stay, signing a pre-contract agreement with the Dons.
The 22-year-old has been on loan with the Grecians since January, but has turned down the chance to secure a permanent move to St James' Park, signing a pre-contract deal with the Scottish Premiership runners-up.
The striker, who made his Bournemouth debut as a 16-year-old in 2009, told Aberdeen's official website that the opportunity to play European football had been a key factor in his decision, with the club's Europa League campaign due to begin on June 30th.
He said: "To get the opportunity to be involved in European football was a big part of coming here and also the plans the manager outlined for the future which are really exciting."
The news will come as a blow to City boss Paul Tisdale, who having seen Stockley net 10 goals in 22 appearances twice offered him a permanent contract at the club.
Towering marksman Stockley may be hoping to settle at Aberdeen after spending so much of his early career on the road with loan spells at nine clubs already, including Portsmouth, Luton and Cambridge.