The 28-year-old is expected to arrive next week after being recommended to the Mariners by Craig Moore, the former Rangers defender.
Mariners head coach Graham Arnold said on his club's official website: "The exposure of giving him the opportunity to play in the A-League and also the ACL (Asian Champions League) was very appealing to him.
"He comes out with a record of a goal every two-and-a-half to three games in Scotland and we're looking forward to John coming out and adding not only another set of legs but quite a deal of experience for our front line."'
Hearts manager Paulo Sergio admitted Sutton's style did not fit in with his tactics and that the move was necessary for the Edinburgh club to reduce their wage bill.
Sergio said: "It was the club's decision and John's decision to move, with the point of view that we save wages we had here."