The new deal gives Grant $3 million this year and makes him a free agent after the season.
Barry Jackson reports the Dolphins explored trading Grant before deciding to restructure his contract.
Grant, 28, is a former sixth-round pick of the Dolphins back in 2016. He was entering the final year of his four-year, $2.48 million rookie contract when the Dolphins signed him to a four-year extension worth up to $24 million in 2019.
In 2020, Grant appeared in 14 games for the Dolphins and caught 36 passes for 373 yards receiving and a touchdown. He also totaled 459 kick and punt return yards and a touchdown.