The deal is for one year and worth $2.1 million, a league source told ESPN's Jeremy Fowler on Monday.
Michel, 27, will be the third running back to sign with Miami this offseason, joining Raheem Mostert and Chase Edmonds. The Dolphins already have Myles Gaskin on their roster, and they tendered Salvon Ahmed as well.
The Dolphins could use a boost to their rushing offense after finishing 30th in rushing yards in 2021. They also finished with the third-fewest average yards before contact and the seventh-fewest average yards after contact in the league.
Miami has spent a majority of its resources this offseason on improving its offense under first-year coach Mike McDaniel, including signing offensive tackle Terron Armstead and trading for wide receiver Tyreek Hill.
In five seasons as the San Francisco 49ers' run game coordinator, McDaniel's offenses ran for the 11th-most yards in the league. Last season, McDaniel's first as offensive coordinator, the 49ers were seventh in the league in rushing and fifth in attempts.
Michel rushed for 845 yards and scored five touchdowns (four rushing, one receiving) for the Super Bowl champion Rams last season.
They acquired him from the Patriots in August for fifth- and sixth-round picks in the 2022 draft. He filled a major need for the Rams after Cam Akers tore an Achilles tendon before training camp.
Michel played sparingly until he moved into the starting lineup in December following an injury to Darrell Henderson Jr. Michel rushed for more than 100 yards twice that month and had another game in which he had 92 yards rushing. Michel's role in the postseason diminished as Akers returned from his injury to reclaim his starting role.
The Patriots selected Michel with the 31st overall pick in the 2018 draft out of Georgia. They had declined the fifth-year option on his rookie contract last May.
In three seasons with the Patriots, he rushed for 2,292 yards and 14 touchdowns.
This will be a homecoming of sorts for Michel, who was a five-star running back at American Heritage School, roughly 20 miles from Hard Rock Stadium.