The 22-year-old joined Dungannon five years ago after impressing for County Tyrone in the Milk Cup tournament.
"Despite being offered a new contact by the club Jamie has opted to sign for Crusaders," said the Swifts.
Crusaders will start the 2017/18 campaign with a Europa League qualifier first leg against FK Liepaja of Latvia at Seaview on Thursday night.
"All the best in the future Jamie and thanks for your commitment during your five seasons at Stangmore Park," added Dungannon on Tuesday.
Glackin's arrival at the north Belfast club follows the close-season signings of Danish goalkeeper Brian Jensen, defender/midfielder Sean Ward and striker Mark McAllister.
Crusaders missed out on a third straight Premiership title last season and boss Stephen Baxter will be determined to regain the Gibson Cup.
Crusaders have snapped up midfielder Jamie Glackin from Dungannon Swifts on a two-year contract.