Garrard signed in March and climbed atop the depth chart in training camp before he was sidelined by a left knee injury that required arthroscopic surgery Aug. 11. In his absence, Tannehill claimed the starting job for Sunday's opener at Houston.
The release of Garrard on Tuesday was confirmed by his agent, Al Irby. The veteran's $2.25 million salary would have been guaranteed if he was on the roster for the opener.
"To all the dolphins fans thx for ur support! Best of luck to all my teammates. Thx for making me feel at home!! Phins up!!" Garrard posted on his Twitter account.
The 34-year-old Garrard returned to practice Monday on a limited basis and said he's not yet 100 percent.
Moore started the Dolphins' final 12 games last year. Their other quarterback is second-year pro Pat Devlin.
Information from The Associated Press was used in this report.