Zwane has signed a three-year contract with Park and is expected to be amongst the new players to be unveiled by the club next week.
The Lions of the North are also targeting striker Collins Mbesuma to bolster their strikeforce before the start of the new season.
An official at Amatuks confirmed that Zwane, who made 24 appearances for the now relegated side last season, has been handed his clearance by the club.
"We met with the player on Wednesday where was granted his clearance,” the official told snl24.com/kickoff.
Zwane's agent Les Mohami also confirmed that his client was on the move, but refused to disclose his destination.
"We are very happy and grateful to Tuks the way they handled the whole situation,” he said. "We got his clearance, but at the moment I am unable to disclose where he is going.”