Allen said the decision was reached "with a heavy heart because of what he does mean to the game of football."
The 32-year-old Lynch told a news conference in his hometown of San Diego: "I am saddened and shocked. I understand that tough decisions have to be made. But I think the decision is wrong."
Lynch played 11 years for the Buccaneers.
Allen said it was decided the "best way to move forward is to allow him the opportunity to talk to other teams and find a home that is best for him and his family."
Releasing Lynch was reported to have saved the Bucs about $4 million in salary cap space.
"I truly believe my best years as a football player are ahead of me," Lynch said. "But in my heart, I'll always be a Buccaneer."