The news was first reported by NFL Network.
Wilson will help to replace Jarvis Landry, who the Dolphins agreed to trade to the Cleveland Browns. The news also comes on the same day that sources said Sammy Watkins intends to sign with the Kansas City Chiefs, Wilson's old team.
Wilson, 25, joined the Chiefs as an undrafted free agent in 2014 and wound up starting 26 games in his four seasons there.
He showed a knack for making big plays when the Chiefs needed them most. Wilson had two touchdown catches in four career playoff games, and he ran for a 55-yard touchdown on a fake punt in a one-point win over the Super Bowl-bound Atlanta Falcons in December 2016.
Wilson had his best season in 2017, when he caught 42 passes for 554 yards and three touchdowns. He had the best game of his career in the regular-season finale against the Broncos in Denver, where he caught 10 passes for 147 yards.
Wilson has 124 receptions, 1,544 yards and 7 touchdown receptions in 55 career games.