Zakuani has signed a four year deal.
Chris Coleman's side will stump up an initial £1 million for the 20-year-old, with another £500,000 dependant on appearances, as well as agreeing a sell-on fee for the highly rated stopper.
Orient boss Martin Ling has given the deal his blessing, insisting that the club could not refuse the money on offer or deny Zakuani the opportunity to star in The Premiership.
"This is an unbelievable deal both for Gaby and the club," Ling told the club's official website.
"He will be a big miss to us having been with Orient for seven years, but we've secured a fair transfer fee for him and we wish Gaby all the best at Fulham.
"This was an opportunity that he could not turn down and it would have been unfair of us to stand in his way.
"Chris Coleman has followed him for nine months and Fulham have had scouts watching him at every one of our home games this season, so they've done their homework and I'm sure Gaby will be a success at his new club."