Al Fayed has transformed Fulham from a third-tier outfit to an established Premier League club since taking over in 1997.
And Khan indicated he will use the same approach at Craven Cottage as he attempts to move the club to another level
Khan said: "I think Mr Al Fayed did an incredible job here over the last 16 years building this to where it is and it's a passing of the baton, so I'm taking it to the next level.
"I think there is a great leadership here and my goal is to sustain that and also to support the business play they have."
The billionaire owner of the NFL's Jacksonville Jaguars did not reveal how much he paid for Fulham, and would not be drawn on manager Martin Jol's transfer budget.
Khan added: "It's very difficult to be specific. I'm not a micro manager. I don't plan on being involved day to day, but I do plan on giving them all the support they need financially to be successful on the pitch."