Rodgers, 25, will get a chance to compete for Miami's third quarterback job, behind starter Ryan Tannehill and veteran backup Matt Moore. He spent time on the Buccaneers' and Jaguars' practice squads last season.
There are various connections that led to the signing in Miami. First-year general manager Dennis Hickey spent the previous 18 seasons working with the Buccaneers. Dolphins coach Joe Philbin coached Aaron Rodgers during Philbin's time with the Green Bay Packers.
It's been a busy Thursday for the Dolphins, who also announced the signings of two wide receivers to one-year contracts: Kevin Cone and Michael Rios. In addition, free agent Nate Burleson will visit with the team Thursday, a league source confirmed to ESPN.com.