The 23-year-old has signed a five-year contract with the Magpies.
The highly-rated midfielder will be included in the Newcastle squad for the clash with Tottenham this weekend.
Anita made his debut for Ajax in 2005.
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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.