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Mayweather confirmed the bout - which will take place under normal boxing rules despite McGregor having never boxed either amateur or professionally - on his official Twitter feed.
The 40-year-old Mayweather announced his retirement after winning his 49th straight bout against Andre Berto also in Las Vegas in September 2015.
Mayweather will reportedly be paid over 100 million US dollars for the contest, which will be broadcast on pay-per-view networks across the world.
McGregor has become one of the most recognisable mixed martial artists in the world since he won the UFC featherweight title in December 2015.
After splitting two high-profile bouts with Nate Diaz, McGregor knocked out Eddie Alvarez to add the organisation's lightweight title in December last year.
The pair first mooted the idea of a fight in a series of exchanges on social media, in which the Irishman urged Mayweather to step up and sign.
Mayweather will not be the first boxing champion to take on challenges from opponents steeped in other combat sports.
Muhammad Ali fought a 15-round draw against Japanese professional wrestler Antonio Inoki in Tokyo in 1976, in which each man was allowed to use his own respective talent.
Given McGregor's non-existent boxing experience and Mayweather's reputation as one of the finest fighters in history, many observers are already predicting a mis-match.
UFC president Dana White told ESPN: "We've been in negotiations now for a while and to be honest the negotiation went smooth. We got the thing done.
"The impossible deal is now done."
White said the fight would be at 154lbs - light middleweight - and added: "It'll be in a ring, it's a boxing event.
"Conor McGregor is a guy who's done a lot of good things over here for the sport and this company and he wanted this and the fans wanted it too.
"I talked to Conor McGregor this morning. He is absolutely 100 per cent positive that he wins this fight and I stopped doubting Conor McGregor a long time ago.
"Floyd Mayweather is 40 years old, he's always had problems with southpaws. Conor McGregor is 27 and he is a southpaw. Whenever Conor hits people, they fall.
"I'm not saying Conor McGregor's going to win. I'm not saying Floyd Mayweather's going to win. But the reason Conor McGregor's as big as he is is he'll fight anybody, anywhere, anytime. He will go after Floyd Mayweather and he will try to knock him out."
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