Fury, the WBC champion, made the offer to his British rival last week, saying he would accept a 60-40 purse split in order to seal the contest.
Joshua's management team, 258, said on Tuesday that they had accepted Fury's offer on behalf of Joshua and his promoter, Matchroom, and are awaiting the champion's response.
They wrote on social media in a message retweeted by Joshua: "258 and @MatchroomBoxing can confirm, on behalf of @anthonyjoshua, that we accepted all terms presented to us by Fury's team for a fight Dec 3rd last Friday.
"Due to the Queen's passing, it was agreed to halt all communication. We are awaiting a response."
Fury made the offer for a 'Battle of Britain' with Joshua after it emerged that rival champion Oleksandr Usyk had ruled out fighting again until early next year.
Joshua suffered his second straight defeat to the Ukrainian in Saudi Arabia last month, and had planned to make a relatively low-key comeback.
Responding last week to Fury's offer, Joshua's promoter Eddie Hearn expressed caution, questioning whether Fury was "serious" about the bout.
Whilst it would certainly represent the most lucrative option for Joshua at this stage of his career, it would also be a major risk given the consensus that he needs to rebuild in the wake of his losses to Usyk.
And while the projected showdown would attract attention, it would not be as lucrative given Joshua's now-diminished status as a former champion and, by now, a significant underdog.