The team also announced it would begin interviews for the position this week. As part of the announcement, the Titans removed the interim tag from Steve Underwood, who was serving as team president and chief executive officer.
Mike Mularkey, who served as the interim head coach after Ken Whisenhunt's firing, will also get a chance to interview for the full-time job, per the release.
"We are building around our young [quarterback], but we need more weapons," Underwood told reporters. "It takes time, but we expect significant progress next season."
Underwood also said the team has 14 finalists for the position.
Webster took over as Tennessee's GM in 2012 but failed to build a roster that was capable of ending the team's playoff drought, which dates back to 2008. Since then, the Titans have finished above .500 only once, and that came before Webster took charge of personnel decisions (9-7 in 2011).
The arrival of Marcus Mariota was a step in the right direction, and Tennessee hopes he can fill the all-important franchise-quarterback void for many years to come. The lack of impact players elsewhere on the roster led to Webster's exit, though.
He stated in early December that he had a good working relationship with controlling owner Amy Adams Strunk and hoped to see the rebuild through, as Paul Kuharsky of ESPN.com noted.
"I would presume," Webster said. "Amy's been real good to me. She's really been very supportive. I'm dealing with [her] a lot and dealing with this whole situation and trying to get this thing turned around."
Just over a week after Webster made those comments, NFL Network's Ian Rapoport reported (via NFL.com's Kevin Patra) the Titans were considering cleaning house after another frustrating season.
Looking ahead, Mariota showed enough positive signs as a rookie to make the team believe he can provide stability at quarterback for many years to come. The franchise will task the new general manager with putting more talent around the signal-caller.
The team's running game struggled to find any semblance of consistency as it worked through a handful of backfield options. None of them did enough to lock down the job moving forward. Also, the passing attack could use another big-play target.
Tennessee ranked in the middle of the pack defensively but didn't make enough game-changing plays to overcome the lackluster offensive numbers in 2015. So the Titans must seek out more playmakers to go along with a solid foundation on that side of the ball.
The likes of Mariota, Dorial Green-Beckham and Avery Williamson give the Titans some promising building blocks, but there's a lot of work to do to get the team back into the playoffs.