The 33-year-old British fighter had hinted at retiring after sixth-round knockout of Dillian Whyte in front of 94,000 fans at Wembley to retain his title on Saturday.
Speaking to Piers Morgan's TalkTV, Fury said he was deciding to leave boxing behind to spend more time with his family.
"I am done. Every good dog has its day," he said.
"Like the great Roman leader said, there will always be someone else to fight. When is enough, enough?
"I am happy, I am healthy. I still have my brains, I can talk, I have a beautiful wife, I have six kids, umpteen belts.
"I have plenty of money, success, fame, glory, what more am I doing it for?"
Fury is unbeaten in 33 bouts and retirement would mean he would miss out on an opportunity to fight for the undisputed crown and with it a chance to cement his status as Britain's greatest ever heavyweight.
Oleksandr Usyk currently holds the other four world heavyweight belts and he is set to defend those titles against Anthony Joshua at some point, with the details of that fight said to be in "the final negotiations".
It was then expected that the winner of that bout would look to take on Fury to unify the division for the first time since Lennox Lewis achieved the feat in 1999.
But Fury says he is happy with the timing of his decision.
"Boxing is a dangerous sport," he added. "You can be taken out with one punch as we saw on Saturday night and it only takes one unlucky blow and you might not get up off that canvas.
"I am quitting while I am ahead. I am undefeated and only the second man in history to retire undefeated heavyweight champion. I am very happy and contented in my heart with what I've done."
Fury has not ruled out competing under a different format and UFC heavyweight champion Francis Ngannou expects a crossover fight to happen next year.
But for now Fury says his only focus is on his family.
He said: "I have been away for the last 10 years all over the world for boxing. When do I get time to be a father, husband, brother or a son? I need this personal time.
"I always said I wanted to walk away on top of the sport and do it on my terms. I didn't want to be the person who maybe should have retired two years ago.
"I wanted to go out with a knockout performance and they will not forget the Gypsy King in a hurry."