He added: “I read the Home Office letters time and time again not believing that we finally have the right to stay.”
A spokesman for York’s Liberal community said they were “over the moon” at the Home Office’s decision.
The family arrived in the UK more than four years ago after Mr Nuuman left Baghdad to take an Iraqi government-funded postgraduate degree at York University.
In a decision that delighted her parents, Yara Nuuman was offered a place at the Brodetsky Jewish Primary School in Leeds last November. The family moved to the city to be closer to the school.
York’s small Liberal Jewish community has been among the most staunch supporters of the Nuumans right to remain in Britain, raising £3,000 on their behalf.
The family claimed asylum last June after the Iraqis had cancelled Mr Nuuman’s funding and visa.