Whyte, a mandatory challenger for the WBC title for several years, had until 6am on Tuesday to put pen to paper after Fury's co-promoter Frank Warren won the purse bids with an offer of $41million (£30million).
The 33-year-old Londoner is entitled to just 20 per cent of the purse and it was rumoured he was seeking a renegotiation to increase his side of the split, but he has now agreed to forge ahead, according to his opponent.
Fury, who claimed the WBC title by stopping Deontay Wilder in February 2020 and made his first defence by knocking out the American last October, has been goading Whyte on social media ever since the purse bids came to light.
And the 33-year-old WBC champion said in an Instagram story on Tuesday morning: "Oh my God. Dillian Whyte's signed his contract for 8million dollars. What a surprise!
"An absolute idiot. Should this even be a talking point? The man signed, for the biggest payday he's ever going to get in his life."
Fury suspects the reason for Whyte's delay may have been some mental ploy to delay the self-styled Gypsy King's training camp ahead of a blockbuster bout that has been reported to be pencilled in for April 23 at Wembley.
Fury added in a sarcastic American accent: "Oh my God, my head hurts from all the mind-games that Dillian Whyte's been playing on me. Oh my God. I'm so sore. I don't know whether I'm coming or going. My training camp's a mess."
Fury, who has not fought on UK soil since outpointing Francesco Pianeta at Windsor Park in Belfast in August 2018, had another message for his foe as he trained alongside Joseph Parker, narrowly beaten by Whyte in July 2018.
Fury added: "I'm going to absolutely bust Dillian Whyte like a cheap f**king water balloon and then when I finish with him, Joe Parker's going to set about him because you're useless, you big dosser. You useless sausage."
Whyte has kept his counsel in response to Fury's barbs in recent weeks and is yet to make any announcement on the fight.
He last fought 11 months ago, avenging a shock defeat to Russian veteran Alexander Povetkin in Gibraltar.