The 21-year-old was sent to Raith on loan last January but picked up a season-ending injury just two games into his Rovers stint.
Jambos head coach Robbie Neilson has now allowed Carrick to tear up his contract at Tynecastle to give him the chance to kick-start his career elsewhere.
Carrick made 54 appearances in a maroon jersey and scored eight goals, including a memorable first-half strike against Hibernian in March 2014.
Neilson told heartsfc.co.uk: “Dale just wants to play football and to get more game-time.
“He’s at an age where he wants to play every week and we can’t guarantee that, so he’s going to move on and I’m sure he’ll get a club no bother at all.
“We wish him all the best and thank him for all his efforts at the club.”