The consistent, hard-working 31-year-old played 276 games for the Cats over 14 seasons, for 182 wins, including the club's 2007, 2009 and 2011 flags.
He won Geelong's best and fairest award in 2005 and 2008.
His departure, along with the Cats' decision to part with Paul Chapman, leaves only six triple-premiership players on the club's list.
They are captain Joel Selwood, Steve Johnson, Jimmy Bartel, Corey Enright, James Kelly and Andrew Mackie.
"Joel has been the ultimate team-first player, and is one of the league's most respected players for the way he competed and played the game," coach Chris Scott said.
"Joel was one of the most critical players in the Geelong teams that claimed the three premierships.
"He did a huge amount of contested work in the midfield and was one of the bravest and hardest players in the game.
"He could easily have chased personal accolades, but he instead always put the team's needs ahead of anything else.
"His teammates loved playing with him and he was a true leader around the club."
Corey said he valued the opportunities and friendships the game had delivered him.
"I have been fortunate to have met outstanding people, from players, coaches, staff and trainers that I am proud to call my friends," he said.
"The club has always put its people first, and has always been there for me, helping my development and challenging and supporting me as both a player and a person."
Corey's retirement comes after the Cats announced recently they would be parting ways with Chapman, two-time premiership defender Josh Hunt and key forward James Podsiadly, who are all looking to continue their AFL careers elsewhere.
THE AFL CAREER OF RETIRING GEELONG STAR JOEL COREY
* Games: 276
* Wins: 182
* Premierships: 2007, 2009, 2011
* Best and fairest: 2005, 2008
* All Australian: 2007, 2008