The extension is worth $19 million with $11 million guaranteed, a source told ESPN's Adam Schefter.
Wake, 35, overcame adversity last year by bouncing back from a season-ending Achilles injury in 2015 to lead the Dolphins with 11.5 sacks. He made his fifth career Pro Bowl as a result and is one of Miami's emotional leaders.
Dolphins vice president Mike Tannenbaum said his biggest priority this offseason was taking care of his own players. Wake is the first major, in-house signing of the offseason. The Dolphins also are expected to discuss contract extensions with leading wide receiver Jarvis Landry and starting safety Reshad Jones. Both have one year left on their contracts.
Miami cleared cap room earlier this week with the release of former defensive linemen Mario Williams and Earl Mitchell.
The Dolphins went 10-6 last season and made the playoffs for the first time since 2008. They lost to the Pittsburgh Steelers in the wild-card round.