The much-anticipated showdown appeared to be in jeopardy after Fury, who turned down a previous date in Saudi Arabia, demanded 70 per cent of the total purse for the revised London date.
But Usyk posted a brief message on his social media on Friday in which he said he would accept Fury's terms provided he makes a £1million donation to those affected by the war in Ukraine.
Usyk said: "Hey, greedy belly. I accept your offer - 70-30 split the fight with you on April 29 at Wembley.
"But you will promise to donate to Ukraine immediately after the fight, £1million. And for every day of your delay you will pay one per cent from your purse to Ukrainian people. Deal?"
Earlier, Fury had posted a video of his own laying out his terms for the contest and insisting Usyk's percentage would fall by one per cent for every day the Ukrainian delayed.
Fury last fought in December when he stopped domestic rival Derek Chisora, while Usyk has not stepped in the ring since he successfully defended his titles with a second straight win over Anthony Joshua in Jeddah in August.
The World Boxing Association tweeted on Friday evening: "WBA president Gilberto Mendoza received confirmation from Oleksandr Usyk and Tyson Fury's teams that there is an agreement to make the unification fight. They request time to work on the contracts to close the deal. #UsykFury"