Miami waived cornerback Zack Bowman in a corresponding roster move.
Coples was cut by the Jets on Monday. He had 16.5 sacks since being drafted by New York in 2012.
Dolphins vice president Mike Tannenbaum drafted Coples in 2012 when he was general manager of the Jets.
Miami will travel to play the Jets on Sunday. Coples knows New York's defensive scheme well and could provide valuable insight for the Dolphins during their week of preparation.
The Dolphins (4-6), who have lost three of their past four games, are in need of help on their front seven defensively. Pro Bowl defensive end Cameron Wake is out for the year with an Achilles tear and outside linebackers Jelani Jenkins (ankle) and Koa Misi (abdomen) missed last week's loss against the Dallas Cowboys with injuries. Miami also is ranked 31st against the run.
The Jets, to fill Coples' roster spot, signed linebacker Josh Martin off the Indianapolis Colts' practice squad on Tuesday.