UFC lightweight champion Conor McGregor says he has signed a "record-breaking deal" to fight Floyd Mayweather Jr.

Now, he says, it's up to Mayweather to do the same to make the megafight happen.

"The first, and most important part of this historic contract has now officially been signed off on," McGregor said in a statement to Themaclife.com. "Congratulations to all parties involved. We now await [Mayweather's adviser] Al Haymon and his boxer's signature in the coming days."

McGregor did not specify the terms of the deal he signed. On Thursday morning, he tweeted about the agreement.

Let's go get some boxing ones now son. pic.twitter.com/KwBkFriTto — Conor McGregor (@TheNotoriousMMA) May 18, 2017

McGregor's confirmation of the signing came just after UFC president Dana White told TNT that McGregor had agreed to the bout.

"The McGregor side is done," White said while appearing as a guest on the network's postgame wrap-up of Game 1 of the Eastern Conference finals. "I'm starting to work on the Mayweather side now.

"I'm not saying the fight will happen, but I've got one side done. Now it's time to work on the other. If we can come to a deal with Haymon and Mayweather, the fight's gonna happen."

White added the much-anticipated bout would be "straight-up boxing."

Conor McGregor says he signed a "record-breaking deal" to fight Floyd Mayweather. Terms weren't announced. ESPN Illustration

Mayweather, who was in London on Saturday as the promoter for Gervonta Davis, reiterated his belief that the fight with McGregor would happen, even stating he would want to see Davis potentially fight on the undercard.

"Well, if me and Conor McGregor do happen to make the fight happen, and I think the fight will happen, I would love this young kid [Davis] on the undercard and Badou Jack on the undercard," said Mayweather, who retired with a 49-0 record. "I had a great career and my career may not be over, and No. 50 may be against Conor McGregor. We'll just wait and see."

Earlier in the week, Mayweather said he was awaiting information from White and McGregor.

"I'm not here to throw anybody under the bus, [and] I can't sit here and say that they are waiting on us," Mayweather said in London. "I'm not saying that. And we're not waiting on them.

"I have a team for [negotiating], but as soon as their side [UFC] communicates with our side, then the fight will happen."

Over the weekend, White told ESPN's Brett Okamoto that his plan was to lock in McGregor by this past Sunday and then move to firm up Mayweather.

"We're right there to get this deal done. We've just got to get the deal done," White told ESPN on Saturday. "I would like to get it done this Sunday and start negotiating with Team Mayweather, and if that deal can get done, then we'll get it done, and if it can't, I need to move on."

While there have been no firm deadlines established for the fight to come together, White has said McGregor wants to fight twice this year.

"He wants to fight twice this year and one of those fights to be Floyd, if possible," White previously told ESPN.

Mayweather on Wednesday said he has designs on McGregor only.

"There's only one fight that makes business sense," Mayweather said. "I came out of retirement because I'm a businessman and I want to give the world what they want to see.

"McGregor's a fighter. I'm a fighter. This is what the fight fans and MMA fans want to see."