The Tennessean reported the contract is for three years and worth $21 million.
NFL Network insider Jason La Canfora reported Tuesday that the Seattle Seahawks were unlikely to re-sign Hasselbeck. Later Tuesday, the team agreed to terms with former Minnesota Vikings quarterback Tarvaris Jackson.
Veteran Kerry Collins retired three weeks ago, and the Titans plan to trade or release Vince Young before training camp opens Friday.
"I think it's a good move," Titans wide receiver Damien Williams said Wednesday as news of the Hasselbeck deal leaked. "Obviously, we've got a bunch of young guys with Jake and Rusty (Smith, a second-year pro), and they're not quite acclimated. We've got a brand-new system, so to bring in a veteran that knows how to adapt quickly, I think that's a good move. Those guys can have someone to learn from."
Not every Titans player was enthused about the move. In a radio interview Wednesday, cornerback Cortland Finnegan praised Hasselbeck's accomplishments but questioned whether he's the right fit in Tennessee.
"He throws the ball with good checkdowns, good intermediate passing game. That's a West Coast offense they run, he throws the ball quick," Finnegan said on WGFX-FM, according to MusicCityMiracles.com. "I don't fear his deep ball. Don't get me wrong, he's great at what he's done. Pro Bowls, All-Pros, even playing in the Super Bowl, but for what we have going, what direction I want to go and the team wants to go, I don't know if he fits what we need, but I'm not the GM, I'm not the front office."
The 35-year-old Hasselbeck played in 14 games last season, throwing for 3,001 yards and 12 touchdowns with 17 interceptions while completing 59.9 percent of his passes. Originally drafted by the Green Bay Packers in the sixth round of the 1998 draft, the three-time Pro Bowl selection has 29,579 passing yards, 176 touchdowns and 128 interceptions while completing 60.1 percent of his throws in 12 seasons.
Hasselbeck comes to Tennessee already familiar with general manager Mike Reinfeldt, who worked in the Seahawks' front office before joining the Titans in 2007, and Locker, who played at the University of Washington, which is located in Seattle.
"From college to the NFL is a big adjustment," Titans tight end Jared Cook said. "To have somebody to learn under, especially somebody as experienced as Matt Hasselback, I think is going to benefit all our quarterbacks."
In the post-lockout rush to complete rosters, the Titans needed to sign nine draft picks, work to keep some of their own free agents and possibly add a veteran defensive tackle, linebacker and safety. They agreed to terms with 14 undrafted rookies Tuesday.
The challenges don't end with signing players, either. The start of training camp will mark the first time players get to work out with first-year coach Mike Munchak and a staff of new assistants.
The Associated Press contributed to this report.