Quinn, the 14th overall pick in the 2011 draft, is heading into the third year of a four-year, $57 million contract he signed with the Rams in 2016.
With the Dolphins, he’ll be on the defensive line with Cameron Wake and Ndamukong Suh, giving Miami a boost to an already-strong group.
Quinn had a fantastic season in 2013, recording 19 sacks, 34 quarterback hits and seven forced fumbles; that season he was named All-Pro and to the Pro Bowl.
He was also named to the Pro Bowl in 2014.
On Thursday, the Dolphins reportedly gave receiver Jarvis Landry and his agents permission to seek a trade; 10 days ago, Miami designated Landry as its franchise player for this year.