McGregor, who is 28 and from Ireland, is a legend in the world of Mixed Martial Arts (MMA). But he is a complete novice as a boxer.
Mayweather retired undefeated two years ago, after defeating Andre Berto and his great rival Manny Pacquiao, from the Philippines.
He is now 40 but there have been persistent rumors over the last year that he would come out of retirement to take on McGregor in a pay-per-view fight which will make them both extremely rich.
Mayweather, whose nickname is Money, has always emphasized that he is only in the sport for the cash and insisted he had no interest in beating Rocky Marciano's record of 49 victories.
Marciano, who was world heavyweight champion in the 1950s, retired undefeated and died in a plane crash in 1969.
Mayweather's victory over Pacquiao was his 49th win.
Now he has finally agreed to meet, McGregor in a boxing ring, on August 26.
When you think about Mayweather-McGregor then realise Golovkin-Canelo is only a few weeks later. pic.twitter.com/NW8y0kn6RE— Daniel Attias (@Dan_Attias) 14 June 2017
MMA fan Sal Mannan said: "This bout is only about money. Hundreds of millions of dollars will be generated through ticket sales and PPV sales.
"For boxing and MMA fans, we know this bout is not about skills, experience or athleticism. Sadly, Conor McGregor will leave the boxing ring as a loser, but will be handsomely rewarded for his brave misadventures in the world of professional boxing," he told Sputnik.
He added: "For UFC fans like me, I'm worried Conor, with his riches, will leave the Octagon for good."
But boxing aficionados have been far less keen on the prospect of the fight.
Former world super middleweight champion Richie Woodhall said he would much rather watch Gennady "GGG" Golovkin's eagerly awaited contest with Saul "Canelo" Alvarez in September.
"Golovkin against Alvarez will be the fight of the year for me. That is going to be a great fight, not like this circus with Mayweather and McGregor," Woodhall told Sputnik.
McGregor's promoter, Dana White, was bullish: "He will go after Floyd Mayweather and he will try to knock him out."
But British boxer Carl Frampton said he did not fancy McGregor's chances: "Boxing and MMA are two different sports. If I am blatantly honest I think if McGregor lands a glove on Mayweather he would be doing very well. Mayweather made people like Pacquiao and Canelo look ordinary."
Conor McGregor looking pumped for August 26th in Las Vegas 😂 pic.twitter.com/0nsrLKL1yK— E5QUIRE (@Dj_E5QUIRE) 15 June 2017
The pair will be fighting at light-middleweight, with standard 10 ounce gloves and there will be no concessions to MMA, a sport in which fighters are allowed to wrestle and even gouge each other.
McGregor has never boxed professionally but was granted a boxing licence in December by the California State Athletic Commission in December and has reportedly been sparring and training for a year.
Leonard Ellerbe, chief executive of Mayweather Promotions, added: "There is a different feel from the Pacquiao fight. It is the unknown factor.
"There is not one place I go to with Floyd where he doesn't get asked the question: 'Floyd, are you going to fight Conor McGregor?' All Floyd thinks about is fighting Conor McGregor."
This guy lives at the back of the gym in a van. Respect to everyone chasing their dreams in this crazy world. Happy Wednesday everybody! pic.twitter.com/HRVhSeuFbK— Conor McGregor (@TheNotoriousMMA) 14 June 2017
McGregor has won 21 and lost three of his 24 MMA contests.
But boxing journalist Steve Bunce said of McGregor: "He would not win an Irish boxing professional title, but this fight is not about credibility or competition or anything to do with traditional sport and that is fine, providing everybody understands that.
"This is a glorious event and perhaps 5 million people in the USA will pay $99 to watch on pay-per-view and 20,000 will pay as much as $25,000 do to watch live in Las Vegas. It will break records and so it should, it is marvelous mayhem."