His agent, Drew Rosenhaus, told ESPN's Adam Schefter, that Rogers signed a one-year contract.
Rogers' signing follows the decisions by Dolphins wide receivers Allen Hurns and Albert Wilson last week to opt out of the 2020 season.
Rogers, 26, spent the majority of his four seasons with the Colts as a punt return specialist, though he had a breakout year as a receiver in 2018, when he caught a career-high 53 passes for 485 yards and two touchdowns.
He suffered a season-ending knee injury against the Tennessee Titans in Week 13 of the 2019 season, finishing with 16 catches for 179 yards and two touchdowns.
Rogers, an undrafted free agent out of Grambling State, averaged 9.2 yards on 60 punt returns with the Colts. Overall, Rogers has 111 receptions for 1,221 yards and five touchdowns in his career.
ESPN's Mike Wells and Cameron Wolfe contributed to this report.