The Arizona Cardinals, who drafted Nkemdiche in the first round in 2016 as the 29th overall pick, waived him on July 27, a day after he arrived at training camp out of shape.
Nkemdiche's one-year deal with the Dolphins is worth up to $1.1 million, a source tells ESPN's Adam Schefter.
Nkemdiche has been recovering from ACL surgery performed in December.
He was a college teammate of Dolphins left tackle Laremy Tunsil at Ole Miss. The Dolphins checked with Tunsil about Nkemdiche's character before making the move and were satisfied with what he told them.
This is the latest reclamation project the Dolphins have taken on during what is expected to be a rebuilding season. They also traded for quarterback Josh Rosen, another former Arizona first-round pick, in April.
Cardinals coach Kliff Kingsbury didn't hold back when asked about how Nkemdiche showed up to camp.
"Not in shape, I guess," the usually reserved Kingsbury said. "And that's kind of where we'll leave it. I mean, he's on [the PUP list] and he's working through that. When he is cleared, we'll work with him."
Nkemdiche, 24, was arrested June 6 for speeding and driving with a suspended license. He has a court date on Sept. 3.
Nkemdiche, whose career has been riddled with injuries, has 44 career tackles and 4.5 sacks, the latter all coming in 2018. The Cardinals did not pick up the fifth-year option on his contract.
ESPN's Cameron Wolfe and Josh Weinfuss contributed to this report.