Osweiler played in six games for Denver in 2017, starting four, and completed 96 of 172 passes for 1,088 yards with five touchdowns and five interceptions. The Bronos went 0-4 in his starts this past season.
He was the Broncos' second-round pick in the 2012 NFL Draft, but with Denver signing Peyton Manning in free agency, Osweiler played in only 13 games in his first three seasons before starting seven games in 2015 after Manning sustained a foot injury.
Osweiler joins quarterback Ryan Tannehill, who started 13 games for the Dolphins in 2016, but missed the entire 2017 season with a torn left ACL.
Dolphins head coach Adam Gase was a Broncos assistant coach during Osweiler's first stint with the Broncos from 2012 to 2015. Gase was Denver's quarterbacks coach in Tannehill's rookie season of 2012 and was the Broncos' offensive coordinator in 2013 and 2014.