The Allams have pledged to take over the club's debts, believed to be around £20million, and make funds available to manager Nigel Pearson in the January transfer window.
The club themselves have yet to confirm the deal but a statement from the Allams read: "Businessmen Assem and Ehab Allam have agreed a Heads of Terms arrangement with Hull City owner Russell Bartlett to take a controlling interest in the Championship club.
"The deal was reached at 7pm last night (Tuesday) after several weeks of negotiations, leaving only the legal processes to be completed by the end of November."
Allam Sr later told BBC Radio Humberside that he expects the legal process to take up to three weeks.
He said: "It's been passed on to the lawyers and the financial people to start the due diligence and the legal procedure. You need two to three weeks with the legal and financial procedure and Christmas is five weeks from now - if we missed the opportunity then we would have lost the lot. Both sides had to make compromises knowing time was not in our favour."
Source: PA
Source: PA