By Kieran Mulvaney
The pair will clash in Las Vegas on May 1 in a fight Mosley (46-5, 39 knockouts) said was the biggest of his illustrious career.
"It's a fight the world wants to see," he said Tuesday during a teleconference with reporters.
After Mayweather (40-0, 25 KOs) defeated Juan Manuel Marquez last September, and Manny Pacquiao of the Philippines defeated WBO welterweight champion Miguel Cotto, it seemed certain that Mayweather and Pacquiao would clash this year.
But negotiations collapsed over Mayweather's demands for random drug testing, and Mosley stepped in to take the Filipino's place.
"I have to be honest, I thought they were going to be able to avoid me," Mosley admitted in a separate call with Reuters.
"I thought they would be able to fight each other and retire. But this is the fight that had to happen. This is a fight of destiny."
Mosley, a former IBF lightweight champion, has fought at welterweight or higher exclusively since relinquishing his lightweight belt in 1999, including seven bouts at light middleweight.
Conversely, Mayweather has fought at welterweight only five times, and his last two contests - the victory over lightweight champion Marquez and a December 2007 stoppage of Britain's Ricky Hatton - came against opponents who were moving up in weight.
Mosley believes his greater experience at higher weights will be to his advantage.
"As a welterweight, he hasn't fought any of the top welterweights," he said. "I'll be the first one."
At the same time, he is not ready to concede that Mayweather, who is renowned for his quickness, will be the faster man in the ring in Las Vegas.
"I think I'm as fast as any fighter out there," he said. "I've always been one of the fastest. I've never been in the ring with Floyd, so I'm just going to do what I do best, be Sugar Shane Mosley.
"He has good hand speed, but I think my hand speed is good too."
(Editing by Justin Palmer)
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