The deal is worth $49 million with $20 million guaranteed, a league source told ESPN NFL Insider Adam Schefter.
Wake, who has one year and $650,000 left on his contract, had skipped the Dolphins' voluntary workouts at the end of April because he wanted a new contract.
Wake, who made the Pro Bowl in 2010 with 14 sacks, has been one of the few bright spots in Miami since the Dolphins signed him in 2009 out of the Canadian Football League, giving him $4.9 million for four years, including $1 million guaranteed.
Wake went undrafted out of Penn State and signed with the New York Giants, but he didn't make it to training camp. He amassed 39 sacks in two CFL seasons and was a two-time defensive player of the year.
The 30-year-old Wake has 122 tackles and 28 sacks in three NFL seasons.