The Houston Chronicle reported the fight, which will be the co-main event, earlier Monday.
This fight will be Cormier's last at heavyweight. He intends to begin cutting to light heavyweight sometime in November.
Cormier, who is ranked No. 4 among heavyweights by ESPN.com, has said repeatedly he will never fight for that title as long as Cain Velasquez is the champion. Cormier and Velasquez are close friends and training partners at American Kickboxing Academy in San Jose, Calif.
In his most recent fight, on April 20, Cormier improved to 12-0 with a unanimous decision over former UFC heavyweight champion Frank Mir. Though he was in control throughout the fight, Cormier did not display his usual explosiveness.
Since that fight it's been Cormier's intention to exit the heavyweight ranks with an impressive victory. There had been talk of a possible bout with Fabricio Werdum, but Cormier told ESPN.com on Monday night that Nelson was always his preferred choice.
"He's the type of guy who will give fans a great fight," Cormier said. "He's a come-forward, knock-you-out type of guy. He's a guy who's not going to be anywhere but in your face.
"I want that and I also want to enjoy it [competing at heavyweight] one more time. I want to enjoy fight week, not having to cut weight, enjoy training camp. Once I start making the weight cut, I won't enjoy it as much as I do now."
Cormier and Nelson recently expressed on Twitter their desire to fight one another. The feud was born on April 27 after Nelson's first-round knockout of Cheick Kongo at UFC 159 in Newark, N.J.
Nelson recently signed a new multifight deal with UFC. Terms of the deal have not been made public.
During the postfight news conference, Nelson, who was being considered for a showdown with fellow slugger Mark Hunt, expressed interest in fighting Cormier.
"I want to fight the best in the world. And fighting Daniel, you know, he's an Olympian, I'd like to welcome him to UFC," said Nelson, who has a professional record of 19-8.
Nelson will be looking to get back in the win column at UFC 166. He had his three-fight win streak snapped, via unanimous decision, on June 15 by Stipe Miocic.
Velasquez will defend his title against former heavyweight champion Junior dos Santos in the UFC 166 main event. It will be the third meeting between them, with each fighter holding a win over the other.