McGregor beat Eddie Alvarez in November to become the first man ever to hold two UFC titles simultaneously.
However, he has since taken an extended break from competition ahead of the birth of his son - Conor McGregor Jr - of whom he posted the first pictures earlier this month.
But the Irishman has not shied away from talking up the possibility of a fight against Mayweather and today has revealed that he has put pen to paper on a contract.
“It is an honour to sign this record-breaking deal alongside my partners Zuffa LLC, The Ultimate Fighting Championship and Paradigm Sports Management,” McGregor said.
“The first and most important part of this historic contract has now officially been signed off on.
"Congratulations to all parties involved.
"We now await Al Haymon and his boxer’s signature in the coming days.”
Mayweather, who has not seen competitive action since 2015, confirmed earlier this year that he would come out of retirement to fight McGregor.
The 40-year-old is one of the world's richest sportsman and now makes his living as a boxing promoter.
But he is still a 49-fight unbeaten boxer and is generally regarded as one of the greatest men ever to lace up a pair of gloves.
McGregor meanwhile has catapulted UFC onto the global stage and is one of the most followed sports stars on social media.
The epic showdown is expected to be the most lucrative fight of all time with some corners claiming it could generate as much as $1billion (£770million) in revenue.
But the bookmakers are not confident that it will be much of a contest with boxer Mayweather favoured at 1/10 while McGregor is as long as 7/1 to get a win.