Previously, Webster tested positive for cannabis while playing for the Harbour Heat in last year's National Basketball League.
"It is an unfortunate situation for Corey, however this is an action we had to take as a club,'' Breakers general manager Richard Clarke said.
"The second positive test breaches the previous agreement between Corey and the club, and he has also breached team protocols and club values. After consultation with Corey we felt the termination of contract was the most appropriate action for all parties.
"This doesn't rule out Corey being a Breaker again in the future, however he now needs to use this time away from the sport to re-evaluate his priorities and make some changes in his life.
"Corey is someone that has made some bad decisions, and is now faced with the consequences of those decisions. He will need to earn back the trust and belief of the players and the club before he could become a Breaker again in the future.''