Mooy had just helped Celtic secure a memorable domestic treble last season, scoring seven goals and providing 11 assists in 42 appearances across all competitions.
He still had one year left on his Celtic contract but has chosen to end his professional career early.
Speaking to Celtic's official website, Mooy said: "While it feels really sad to be leaving the game, I just feel the time is right for me. I have been so fortunate to enjoy such a great career across the last 15 years, creating some fantastic memories.
"I am delighted to finish my career on such a high with Celtic and I would like to thank all the fans for the great support they gave me during the past year - I was delighted to be part of such a memorable season.
"I hope Celtic continue to dominate the game and I wish Brendan [Rodgers], the new manager great success with the great group of lads at the club."
Mooy played at two FIFA World Cups and represented Australia on 57 occasions.
The former Huddersfield Town and Brighton and Hove Albion man added: "Playing for my country is something I have loved too and of course I will miss the international set up and so many great people who are involved there.
"I have been fortunate to win a number of caps for my country and this has been really important to me – of course I wish Australia nothing but success for the future and I am sure they can get better and better.
"There are too many people to thank who have played such an important role in my career, so many managers, coaches, staff and fellow players. I have been very privileged to be part of some fantastic football environments, all created by really good people.
