Edmonds, 25, totaled a career-high 903 yards from scrimmage and scored twice on 159 touches in 12 games last season for the Arizona Cardinals. The 5-foot-9, 210-pound playmaker entered the league as a fourth-round pick by the Cardinals in the 2018 NFL Draft.
Edmonds totaled 2,472 yards from scrimmage and 14 scores in 57 games over his four-year tenure in Arizona.
The Dolphins posted the third-worst rushing offense in the NFL last season. Myles Gaskin, the team's leading rusher, ran for 612 yards and three scores on 173 carries. He is signed through 2022.
Duke Johnson, Phillip Lindsay, Malcolm Brown and Salvon Ahmed were among the other running backs on the team's roster last season.
The Dolphins agreed to a one-year extension earlier this month with Ahmed. Johnson, Brown and Lindsay are expected to become free agents Wednesday.
The Cardinals signed running back James Conner to a three-year contract extension Monday. Eno Benjamin, Jonathan Ward and Jaylen Samuels are among the other running backs on their roster. Ward and Samuels are signed through 2022. Benjamin is signed through 2023.