Financial terms were not disclosed.
Branch, 30, was released by the Miami Dolphins on March 7 in a salary-cap move.
The Dolphins signed Branch to a three-year, $24 million deal in March 2017 after a promising 2016 season in which he finished with 5.5 sacks. However, after Branch totaled just six sacks over the past two seasons, Miami made the decision to part ways with his $7 million salary for 2019.
His 1.5 sacks in 2018 were his fewest in that category since his 2012 rookie season with the Jacksonville Jaguars, when he had one.
In seven seasons he has 25.5 sacks, eight forced fumbles and 187 tackles in 95 games (39 starts).
ESPN's Cameron Wolfe contributed to this report.