The 19-year-old has previously been strongly linked with a move to Dutch giants Ajax.
David underwent a medical in West London on Friday.
Dutch side Twente have confirmed that the youngster has now joined Fulham.
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Liverpool have unveiled their new home kit for next season, sticking with the hugely popular retro styling of the current shirt.
The reputation of the Premier League means it is the most popular and one of the most watched leagues in the world.