The 26-year-old Edwards was selected by the Bills in the third round of the 2007 NFL Draft struggled with injuries and consistency. He completed 29 of 52 passes with one touchdown and two interceptions in two games this season.
Garrard has also struggled, completing 44-of-74 passes for 448 yards, four touchdowns and five interceptions this year.
Linebacker Alvin Bowen was waived by the Jaguars, who are 1-2, to make room for Edwards on the roster.
(Reporting by Simon Evans in Miami; Editing by Frank Pingue)