Tyson agreed the bet with Paul himself on social media, who initially called The Gypsy King out for wanting to bet $100k.
The wager concerns Paul's upcoming match-up with Tyson's brother, Tommy Fury, with the pair set to fight at Madison Square Garden on 6 August.
The bout was originally slated for December last year, only for Fury to pull out with an illness.
Tommy, a former Love Island star, is still in the early stages of his professional boxing career, and will now meet the equally inexperienced Paul after months of trash talk on both sides.
While Jake is still new to the professional ranks, he's already racked up some impressive knockout wins over former UFC stars Tyron Woodley and Ben Askren.
His 23-year-old opponent has a record of eight wins from eight fights so far, with four coming by way of knockout.
The wager between Tommy's older brother Tyson and Jake first came to be after the pair had a back and forth on Twitter.
Paul branded the WBC world champion a 'f*****g p***y' after Tyson – who is worth £50.5 million according to Forbes – initially put £100k on the line.
"So guys, Tyson Fury who made $40million [£32.6m] last year is willing to bet $100k [£81k] on his brother," the 25-year-old wrote on Twitter.
"Oh my god we’re shaking! Hey Tyson you f***ing p***y, you made $40m, I know it wasn’t as much as me but let’s up the ante.
"Two million, three million, however much you want to bet, are you down? Make a deal."
Fury was quick to respond, as he then questioned whether the American would be able to cough up the cool $1m [£815k].
In a video published on social media, he barked back: "This is a message to Jake Paul. Hey Jakey boy, I hear you want to make a big bet on $100k.
"You want a bigger bet motherf***er? You want $1m? Let's do it. Holla at your boy. If you want $1m, you got it.
"And hey Jakey, I want to see this million dollars in escrow sucker. Because I don't think you've got a million dollars."
Paul, not one to back down from a challenge, quickly fired back at the 33-year-old, even referring to $1m as 'chump change'.
"You want to bet $1m? OK you got it. For the heavyweight champion of the world, a million dollars, and that's all you want to bet?," Paul stated in a follow-up video.
"If you want to go with some chump change like that, no problem.
"I'm already in contact with your lawyer Robert [Davies] and my team is in touch with him so we're gonna get the money into escrow and make it happen right away."
Featured Image Credit: Twitter/@Tyson_Fury/@jakepaul