Branch, 26, started nine games last season for the Jacksonville Jaguars and had four sacks. He missed the first three games of the season after suffering a sprained MCL during the preseason.
He made one of the team's biggest plays of the season when he knocked the ball out of Indianapolis Colts quarterback Matt Hasselbeck's hand and returned it for a touchdown that sparked the Jaguars to a 51-16 victory in December.
Branch recorded 14 sacks in four seasons with the Jaguars after being selected in the second round of the 2012 draft.
As a rookie, Branch was criticized for not giving consistent effort and was challenged to be more consistent when Gus Bradley took over as head coach. Branch responded in 2013, recording six sacks, 37 tackles and three pass breakups.
He burst out of the gate in 2014, getting three sacks and two forced fumbles in the first three games. However, he did not record a sack in the next four games and then missed seven of the final nine games of that season after suffering a groin injury.
Williams signed a $17 million, two-year deal with Miami last week, and Wake is coming back from a torn Achilles tendon. Both are four-time Pro Bowl ends.
Miami's pass rush needs an upgrade under new coach Adam Gase. Last season, the Dolphins tied for 25th in the NFL with 31 sacks.
ESPN Jaguars reporter Michael DiRocco and The Associated Press contributed to this report.