"[This] move is bittersweet, but I leave in great health, excited and energized for my next opportunity," Faine told the team's official website. "I look forward to seeing Josh Freeman and some of the other young talent become bright stars in this league."
Faine has started every NFL game in which he has appeared, a total of 117 in nine seasons.
The Bucs acquired Faine as an unrestricted free agent in 2008. The 30-year-old spent two years in New Orleans after spending three with the Cleveland Browns, who drafted him out of Notre Dame with the 21st overall pick in 2003.
"I appreciate the leadership Jeff has provided to our franchise, both on and off the field," general manager Mark Dominik said. "He has been a true professional during his time here. We wish him all the best and are confident he will have continued success in the future."