The two-minute production features various scenes from both of their notorious careers and plenty of trash talk from the larger-than-life athletes.
McGregor and Mayweather will battle on Aug. 26.
"I'm going to stay at the top," said Mayweather, who is 49-0 as a boxer. "Do what I want to, because when you speak boxing, you are speaking Mayweather."
Mayweather retired from the sport in 2015 after beating Andre Berto.
"I'm going to be ruthless in there," said McGregor, who is 21-3 in UFC. "My fist is just going to break his whole face and that's it."
McGregor beat Eddie Alvarez in November during UFC 205.
"You've got MMA fighters calling me out. Man, stay in your lane," Mayweather said in the video.
"Let's not kid ourselves here, who the big star is of this show," McGregor said in the video. "You've got me, a slick handsome Irish kid and has climbed to the top of the game. Quicker than anyone else has done it."
"This is not like a normal fight," Mayweather said.
"It's big, big business," McGregor said.
"I'm always looking to make history, every single day," McGregor said. "Here we are again. More history."
McGregor's win against Alvarez made him the first simultaneous two-division champion in UFC history.
The two fighters will be on a world tour, meeting face-to-face on Tuesday in Los Angeles, on Wednesday in Toronto, Canada, on Thursday in New York and on July 14 in London, England.
The pay-per view mega-fight will be a 12-round bout at 154 pounds. Mouthes will shut and punches thrown at the T-Mobile Arena in Las Vegas.