Cohen who spent four seasons with Ezenkosi before their recent relegation, has signed a two-year contract with the Students.
The Johannesburg born defender's agent from Stella Africa, Steve Kapeluschnik confirms that Cohen has joined Wits.
"Larry's contract with Cosmos expired last month so he was able to join Wits as a free agent. He has had a wonderful four seasons with Cosmos but was unlucky not to play much this past season due to injuries."
Talking to Kickoff.com, Cohen extended his sincere thanks to Jomo Sono for introducing him into top flight football.
"Playing for Jomo Cosmos was a privilege but being coached by the master (Jomo Sono) himself was an even greater honour.
"I am highly motivated following my move to Wits and am looking forward to a great stay and achieving success with my new team, he adds.