The Briton, 28, withdrew from a rematch with Ukrainian Wladimir Klitschko, scheduled for 29 October, because of reported mental health issues.
Fury, who holds the WBA and WBO titles, faces a hearing in November into a charge for an alleged doping violation.
"Boxing is the saddest thing I ever took part in," read his tweet, adding: "I'm the greatest, and also retired."
Fury had been scheduled to earn the biggest purse of his career for his second fight with Klitschko at the Manchester Arena this month.
He postponed the original rematch against the Ukrainian, which was scheduled for July, after injuring an ankle in training.
He has been given 10 days by the World Boxing Organisation to provide detailed reasons for his second withdrawal.
Boxing pundit Steve Bunce told BBC Radio 5 live: "I think this is more than goading the media and the public. I think he is jumping the queue before people start taking his belts.
"Tyson Fury feels he has been overlooked, neglected, under-loved, but he has fuelled it by saying things which are stupid.
"He will probably come back in two years' time but what type of boxer he will be then I have no idea."
BBC boxing correspondent Mike Costello added: "It is not the first time Fury has made such remarks and it might not be the last.
"Fury's announcement clears the way for the WBO and the WBA to make plans for their vacant titles with Klitschko against Anthony Joshua a distinct possibility."
Fury's announcement has opened up debate in the sporting world on social media, with England cricketer Ben Stokes tweeting "Fury is an embarrassment to professional sport".
British promoter Eddie Hearn said Fury would never fight again, prompting his trainer and uncle, Peter Fury, to state his nephew would return to the ring next year.
Fury is under investigation, having been charged by the UK Anti-Doping Agency (Ukad) in June, after traces of a banned substance were allegedly found in a urine sample.
The fighter has denied allegations of doping.
It has also been alleged he refused to give a sample, having been visited by Ukad. An athlete who refuses to take a drugs test can be banned for four years.
In November, Fury beat Klitschko on points in Germany - the 40-year-old's first loss since 2004 - to gain the WBA, IBF, WBO and IBO titles, with American Deontay Wilder holding the WBC belt.
Within two weeks Fury was stripped of the IBF title because he was unable to fight mandatory challenger Vyacheslav Glazkov - and that belt is now held by rival British world heavyweight champion Joshua.
(BBC)
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