It will give Grant a big raise over the $720,000 in base salary he was scheduled to make this season and keep him under contract through the 2023 season.
The former sixth-round choice was scheduled to become a free agent in March.
The Dolphins already signed another member of their 2016 draft class, getting cornerback Xavien Howard locked up with a five-year, $75.3 million extension this offseason. They are expected to pursue a long-term deal with left tackle Laremy Tunsil, too, after picking up his fifth-year option for 2020.
Grant has 34 catches for 471 yards and four touchdowns in three seasons but has returned two punts and a kickoff for touchdowns.
He returned to practice this week after missing the first two preseason games with a hamstring injury.