White later confirmed the news with ESPN.com. The bout will be held at UFC 140 in Toronto.
"I'm excited for the fight," Jones told ESPN.com. "To beat three UFC champions in the same year would be an absolute blessing in so many ways.
"I'm not even sure it's been done before. That would be cool. I'm already looking forward to that."
The fight will be Jones' fourth this year and his second title defense. He retained his belt on Sept. 24 with a fourth-round submission of former champion Quinton Jackson at UFC 135 in Denver.
"Outside of all my past achievements, I have to look at Lyoto as an absolute individual. I am aware that I just beat the two people who beat him," Jones told ESPN.com.
"But styles make fights and I have to respect Lyoto. He went on a long tear being undefeated; he's a tough guy."
In 19 professional fights, only Jackson and Rua have beaten Machida. It was Rua who handed Machida his first professional loss and ended his brief reign as UFC light heavyweight champion on May 8, 2010.
During his most recent appearance inside the cage, Machida (17-2) ended his two-fight skid with a first-round knockout of Randy Couture at UFC 129. That bout was held April 30 in Toronto.
"Stylistically, he matches up well with Jones," Machida's manager, Ed Soares, told ESPN.com. "The guys Jones has been fighting stand in front of him.
"The way Machida moves around the Octagon makes him a different type of fighter. Lyoto has the tools and the experience and the techniques to be able to beat Jon Jones."
Jones was expected to make his next title defense against Rashad Evans. But the former light heavyweight champion, and Jones' ex-teammate, is recovering from a hand injury.
Franklin McNeil covers mixed martial arts and boxing for ESPN.com. Follow him on Twitter at www.twitter.com/Franklin_McNeil