The deal was agreed to verbally on Wednesday, Morrison's agent, Bruce Tollner, told the Associated Press.
Listed at 6-foot-2 and 240 pounds, Morrison is a six-year starter, who spent last year with the Jacksonville Jaguars, who elected not to re-sign him this offseason.
"He's fired up," Tollner said. "He's been working out for quite a while and has had several offers from other teams. He's excited to be going to Buffalo."
The Bills have not confirmed the deal as they have a policy of not announcing acquisitions until the player has been signed.
The agreement comes a day after coach Chan Gailey said Torbor was having "some things taken care of medically." Gailey did not go into further detail.
A backup inside linebacker, Torbor has not been present for the past two days of practice as Buffalo prepares to host Jacksonville in a preseason game Saturday.
The Bills have already retooled the inside linebacker position by signing eight-year veteran Nick Barnett earlier this month to replace the free-agent loss of Paul Posluszny, who's now with the Jaguars.
Morrison was selected in the third round of the 2005 draft by Oakland, and spent the next five seasons with the Raiders.
Morrison struggled in his one season with the Jaguars in which he had no sacks or interceptions. His most memorable game came against his former team on Dec. 12, when he was credited with seven tackles in a 38-31 win over the Raiders.
The Jaguars were considering re-signing him before they signed Posluszny to a six-year, $45 million contract last month.
Overall, Morrison has five sacks and seven interceptions in 96 career games.
Morrison is the second player the Bills added on Wednesday after the team addressed its banged-up group of receivers by signing free agent Ruvell Martin.
Martin has five seasons of NFL experience after spending last year with Seattle. He has 65 catches for 1,006 yards and seven touchdowns in 53 games, including nine starts.
A Saginaw Valley (Mich.) State product, Martin has also played with Green Bay and St. Louis.
The Bills are in need of healthy receivers as they prepare to host Jacksonville. Receivers Roscoe Parrish (left calf), Donald Jones (head), Naaman Roosevelt (right ankle) and Craig Davis have all missed the first two days of practice this week.
Buffalo's receiving corps has already been depleted after the team traded seven-year veteran Lee Evans to Baltimore two weeks ago.
Martin practiced with the team on Wednesday, and is expected to get some playing time -- mostly on special teams -- Saturday, Gailey said.