Quinn was among the cuts made by the Dolphins on Tuesday, when the team made 11 moves in order to meet the NFL's deadline for paring the roster down to 75 players.
Quinn was on the practice field with the Dolphins in the morning, then announced the news on his Twitter account about two hours after that session ended.
"It was short lived but I enjoyed every second," Quinn wrote on Twitter. "Thank you Miami Dolphins for the opportunity to play the game I love again. Best of luck to all the players and coaches this season!"
Dolphins coach Joe Philbin said before the cuts were announced Tuesday that he was hardly looking forward to the idea of telling some players that they were not making the team.
"Yeah, that part of it is difficult," Philbin said. "You do your best to talk to the players about the NFL and hopefully their careers can be a long-term thing. There's always setbacks in life and you deal with them and you move on. Certainly, there will be some quality individuals that you have to let go."
The Dolphins signed Quinn on Aug. 12. He completed all four of his pass attempts for 22 yards in his lone preseason appearance for Miami, which famously decided not to take him in the 2007 draft -- even though Quinn was under the assumption he was Dolphins-bound. The decision was booed by some fans in the crowd at Miami's draft party, as well.
Quinn was brought in this time to challenge Matt Moore for the No. 2 quarterback spot in Miami behind starter Ryan Tannehill. And this move makes it clear, Moore won that battle.
Moore will likely take at least some of the snaps when Miami plays host to St. Louis on Thursday night in the preseason finale for both cuts.
Tannehill said he's learned from having Quinn around, even for a short time.
"He's been around the league," Tannehill said. "He kind of brings a veteran perspective on some plays that maybe he's run in the past. ... To have a veteran guy with that kind of knowledge has been good."
Miami was the seventh NFL club to bring in Quinn, who only has seen regular-season action with two franchises -- the Browns, from 2007 through 2009, and Kansas City in parts of 10 games during the 2012 season.