"Greg brings a track record of success and is a proven player who can help strengthen the offense," general manager Dennis Hickey said in a statement.
Jennings visited with the Dolphins earlier this month and left without a contract. He reportedly met with other teams, such as the Carolina Panthers and New Orleans Saints, but decided Miami was the best fit.
He played under Dolphins coach Joe Philbin when Philbin was the offensive coordinator with the Green Bay Packers.
Jennings signed a five-year, $45 million deal with the Vikings in 2013, saying he wanted a fresh start after playing his first seven seasons with the Packers. But after playing with four different starting quarterbacks in his two seasons in Minnesota, Jennings caught just 127 passes for 1,546 yards and 10 touchdowns.
Jennings' abbreviated tenure in Minnesota began with a spat with Packers quarterback Aaron Rodgers, whom Jennings refused to mention by name in a series of interviews. The receiver called Rodgers "12" and "the guy they have now" when asked to compare playing with Rodgers and Brett Favre and later lobbed criticism at Rodgers in an interview with the Minneapolis Star Tribune. Jennings later apologized publicly for the comments, and the two shared a lengthy embrace after Jennings' first game against his former team.
In seven seasons with the Packers, Jennings caught 425 passes for 6,537 yards and 63 touchdowns.
Miami had one of the NFL's youngest receiving corps led by Kenny Stills (22), Jarvis Landry (22) and Rishard Matthews (25). Jennings, who is entering his 10th season, is a proven veteran who can serve as a mentor for his fellow receivers on and off the field.
ESPN.com Vikings reporter Ben Goessling contributed to this report.