The signing was announced Tuesday after Branch visited the team's facility.
Listed at 6-foot-6 and 325 pounds, Branch enters his seventh NFL season after spending the past two as a starter with the Seattle Seahawks. He played his first four seasons in Arizona after being selected early in the second round by the Cardinals in the 2007 draft out of Michigan.
He had four of his eight career sacks with the Seahawks.
Branch is regarded as a solid run stuffer, and has the versatility of being able to play every defensive line position.
The Bills' defense is in transition under new coordinator Mike Pettine, who's noted for his aggressive approach with the New York Jets.
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