Mr Gill, a self-confessed Manchester United fan, succeeds Robin Launders, who left in the summer to become chief executive of rival Premiership club Leeds United.
In a separate move, First Choice named Lance Moir, a former corporate finance director at brewing and leisure giant Bass, as Mr Gill's replacement.
Mr Gill, 39, is understood to have played an instrumental role in the ousting of Francis Baron, the First Choice chief executive deposed last month in a boardroom coup.
One of Mr Gill's first tasks will be to improve the flow of information between Manchester United and institutional investors. Since Mr Launders' departure Manchester United has been the subject of persistent takeover rumours.
At one stage the rumours got so out of hand that the club even took the highly unusual step of issuing a Stock Exchange statement saying that no bid approaches had been received.
Both Mr Gill and Mr Moir will take up their new posts in the new year. Mr Gill will stay on to help present First Choice's annual results due tomorrow.