The Premier League has approved the sale, with current owner Mohamed Al-Fayed due to speak to the media tomorrow afternoon.
In a statement to The AP, Khan said: "Fulham is the perfect club at the perfect time for me. I want to be clear, I do not view myself so much as the owner of Fulham, but a custodian of the club on behalf of its fans.
"My priority is to ensure the club and Craven Cottage each have a viable and sustainable Premier League future that fans of present and future generations can be proud of.
"We will manage the club's financial and operational affairs with prudence and care, with youth development and community programs as fundamentally important elements of Fulham's future."
Khan, who also owns NFL franchise the Jacksonville Jaguars, is reportedly worth an estimated £1.65b.