Miami confirmed the signing on Wednesday. Sterup's agent, Brett Tessler, announced the signing on Tuesday, via Twitter.
Sterup entered the NFL as an undrafted free agent signing by the Kansas City Chiefs in 2016. He joined the Browns' practice squad on Sept. 9 after being waived on Sept. 7. He also spent time on the New York Jets' practice squad.
Sterup was a two-year starter at Nebraska. The 6-foot-9, 318-pound offensive lineman will add depth to the Dolphins' offensive line, which lost right tackle Ja'Wuan James to a hamstring injury during Sunday's loss to the Oakland Raiders.
The Dolphins are currently starting Laremy Tunsil at left tackle, Jesse Davis at left guard, Mike Pouncey at center and Jermon Bushrod at right guard. Before the Sterup signing, the Dolphins just had Sam Young, Ted Larsen, Jake Brendel and Isaac Asiata serving as backups, according to the team's depth chart.
Miami lost 27-24 to the Raiders on Sunday, it's first game since trading away Pro Bowl running back Jay Ajayi. The Dolphins had 86 rushing yards in the loss.
"We had a couple of runs that popped out of there," Dolphins coach Adam Gase said after the game. "I feel like they had a couple of good runs, but we had those penalties on a couple of good ones. We did good in the passing game. With what they were doing outside, they were trying to take away ... DeVante [Parker] and Jarvis [Landry] were on the same side. They were playing some coverages where it left the backs one-on-one with the linebackers and that was a good matchup for us."
The Dolphins battle the Carolina Panthers at 8:30 p.m. on Monday Night Football at Bank of America Stadium in Charlotte.