The quarterback was brought in to compete with Tavaris Jackson to be the NFC West side's backup.
The 28-year-old wrote on Twitter: "Want to thank the Seahawks organisation, coaches, teammates and especially the fans for a great off-season.
"It was such a blessing to be a part of such a special group! Thank you for the opportunity and best of luck this season! God bless!"
Quinn was drafted by the Cleveland Browns in 2007 and has since had spells with the Denver Broncos and the Kansas City Chiefs.