The 22-year-old will officially become a Dons player on July 1 when his contract at Sky Bet League One club Swindon ends.
Storey scored 13 goals while on loan at Inverness Caledonian Thistle last season, finishing the campaign as the club's leading goalscorer.
He made 37 appearances for Swindon during a five-year spell and has also spent time on loan at Shrewsbury, Portsmouth and Newport County.