The father and son team succeed Russell Bartlett, whose three-year tenure at the club began with promotion to the Premier League but turned sour last season as the club's mounting debts were compounded by relegation back to the Championship.
Assem Allam said: "I'm very pleased we managed to achieve the deal. We wanted to give a present to the fans of Hull City. We would like the fans to be patient. Our investment exceeded what we initially thought so my plans for the club will have to be delayed."
The Tigers finished the 2009/10 campaign approximately £35million in the red and were forced to sell a number of key players, reducing the debts to around £20million.
Bartlett made no secret of his desire to sell the club as the board battled to keep Hull out of administration, and Friday's news means that threat has now been removed.
It was announced on November 10 that a deal had been agreed between Bartlett and the Allams, but it has taken a further five weeks for the process to be completed.
After dealing with Hull's debts, the new owners' first priority will be to ensure Nigel Pearson's side remain in the Championship.
The Tigers currently sit 19th in the table, three places and two points above the relegation zone.
Pearson has been assured his job is not under any immediate threat and he will be handed a limited transfer kitty in January.
Source: PA
Source: PA