Branch's agent, Blake Baratz, told ESPN NFL Insider Adam Schefter that the contract is worth $3 million and includes $350,000 in incentives.
Branch has started 31 games over the past two seasons for Seattle, registering 64 tackles and four sacks, including a career-best three in 2011.
Buffalo's defense last year was a major disappointment, primarily due to its porous run defense. The Bills were 31st in the NFL versus the run in 2012, allowing 145.8 yards per game. The Bills expect to run a mix of 3-4 and 4-3 defenses next season under new defensive coordinator Mike Pettine.
Branch was selected in the second round of the 2007 draft by the Arizona Cardinals but started just three games in four seasons before becoming a regular with the Seahawks.
Information from ESPN NFL Insider Adam Schefter and ESPN.com AFC East blogger James Walker was used in this report.