The two have been in talks for weeks ... but now we're told from both camps that it's a done deal and the two will fight in Vegas on September 12th.
We spoke with Berto who tells us, "It's a pleasure and honor to be in this position and I'm looking forward to capitalizing on every moment of it".
As we previously reported, there's some bad blood between the two -- with Berto claiming Mayweather had been crank calling his phone ... and he believes it was all over a woman.
Mayweather is 48-0. Berto is 33-3.
Story developing ...