Agent Gary Wichard confirmed the deal in an e-mail to The Associated Press on Tuesday night and the team officially announced the signing on Wednesday.
Losman's deal led to the release of third-string quarterback Mike Teel. A team spokesman said Wednesday night that Teel had been waived. Seattle drafted him in the sixth round last year out of Rutgers. The Seahawks already released Mike Reilly, a former Central Washington quarterback just recently picked up on waivers from the St. Louis Rams.
Hasselbeck is 34 and entering the final season of his contract. He threw a career-high 17 interceptions last season while getting battered for the second consecutive year.
"I am real pleased with Matt being our quarterback right now and being in the lead position," Carroll said Monday. "However, we are trying to make it as competitive as possible. We are trying to push Matt to make him better and try to elevate Charlie's game as well. That is just the way we are doing it. It will always be a competition in my mind."
Losman, 29, played last season for the Las Vegas Locomotives of the UFL and was signed to finish the season with the Oakland Raiders. He was the Bills' first-round pick in 2004 and had 33 career starts in five seasons with Buffalo.
Losman's only full season as a starter was 2006 -- not counting his 2009 UFL championship season with the Locomotives. Known for his strong arm, he threw 19 touchdowns and 14 interceptions in '06 for Buffalo. The Bills then drafted Trent Edwards, and Losman soon wanted out of Buffalo.
Carroll has also acquired LenDale White, his former star running back at Southern California, while adding former New York Jets All-Pro Leon Washington at a running back position that now has six veterans.
At wide receiver, Carroll has signed Reggie Williams and Mike Williams out of free-agent tryouts. Both are failed former top-10 overall picks getting a new NFL life behind leading receiver T.J. Houshmandzadeh.
John Clayton is a senior NFL writer for ESPN.com. Information from The Associated Press was used in this report.