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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Summer 2016 is set to be a very exciting time for football fans, as this is when the long awaited Euro 2016 tournament kicks off.
Since Guus Hiddink arrived at the helm, Chelsea have improved considerably after a tricky start to the campaign.