The Jacksonville Jaguars owner hailed the 84-year-old as "incredible" after guiding the club from the third tier of English football to Premier League regulars since 1997.
The 84-year-old took over at Craven Cottage in 1997 and led the club from the third level of English football to the Premier League. The Cottagers have remained in the top flight since 2001, achieving a highest finish of seventh in 2009 and reaching the final of the Europa League in 2010, and Khan promised to build on the Egyptian's work.
"I think it [what Al Fayed has done] is incredible," Khan told Sky Sports. "The man rescued Fulham and had a great vision which he's shared with me. I think it's very, very important to all the Fulham fans.
"I really enjoyed getting to know him. He's a wonderful guy, very much to the point. The conclusion [of the deal] came very quickly and amicably.
"There's a great leadership here and I have a lot to learn. But I'll give the team all the support it needs to be successful on the pitch."
Khan, who also owns the NFL's Jacksonville Jaguars, said the takeover is something that will last long in his memory but refused to reveal how much he had paid to acquire the club.
"I think what has happened has been absolutely incredible, something I'm going to remember forever," Khan said. "[The purchase price] is highly confidential. It's a very special place. This is the perfect club for me at a perfect time. It's the passing of the baton, taking it to the next level."