Under a right of first refusal clause the Eagles put into Babin's contract, they had one week to match the offer sheet signed Wednesday. Without the clause, Babin would be an unrestricted free agent because of his six years of NFL service.
The Titans announced that Philadelphia notified the NFL on Friday it would not match the offer.
"We're happy our deal with Jason worked out," general manager Mike Reinfeldt said in a statement. "He's a high-energy player and a good pass rusher, and he fits what we do very well. He has all offseason to come in and work with Coach [Jim] Washburn and become a part of our rotation at defensive end."
Babin, a first-round draft pick in 2004 out of Western Michigan, has played for Houston, Seattle, Kansas City and Philadelphia. Last season, the 6-foot-3, 267-pound end played in 12 games and had 20 tackles and 2½ sacks for the Eagles.
Babin said he had been trying not to think too much of the deal, not knowing if the Eagles would match the offer. He said in a statement he was ecstatic and can't wait to start working with the Titans and Washburn.
"The style of defense the Titans play, as far as what the defensive line does and the way they want their guys to play, it suits my abilities. They get wide, they come off the ball, they rush the passer, and they're aggressive. To me, it's just a natural fit," Babin said.