Congratulations to all parties involved.
White, appearing on TNT's postgame coverage following Game 1 of Celtics-Cavaliers playoff series, said "The McGregor side is done". "I'm starting to work on the Mayweather side now".
McGregor and the UFC have been locked in talks over a split of the purse the fighter would earn from a fight with Mayweather, which will be in a boxing rules contest.
White now must strike a deal with Mayweather's team.
The UFC president was still cautious about saying if the fight would happen but he said the wheels were officially in motion. Although the UFC and McGregor have come to terms, White hasn't yet figured out the Mayweather side of the equation, which is likely to be much more complex. "Now it's time to work on the other", White said.
In a statement given to Themaclife.com, McGregor described the deal as "historic" and placed the ball firmly in Floyd's court.
"If we really do get down on that time frame, then it couldn't possibly happen", White told Jim Rome in the latter's CBS radio show.More news: Skoda Karoq drip-feed continues with new close-up images
Many from within boxing have questioned whether McGregor could compete with Mayweather, who retired unbeaten in September 2015 after 49 professional contests.
Conor McGregor fighting Floyd Mayweather took a step closer to reality this morning.
America's Mayweather is accompanying his protege Gervonta Davis in London, where on Saturday he makes the first defence of his IBF super-featherweight title against Liam Walsh.
McGregor's chances in the bout have been repeatedly dismissed and many believe should the fight happen it will be completely one-sided.
"I came out of retirement because I'm a businessman and I want to give the world what they want to see".
White's words, of course, are often taken with a grain of salt by MMA's rather untrusting fans.