The 16-year-old defender is rated as one of the brightest up-and-coming talents in Europe, and has already earned eight caps for the Holland U17 side.
A number of clubs from across the continent wanted to secure Bazoer's signature, after he announced his intentions to leave PSV Eindhoven, with Red Devils boss Sir Alex Ferguson monitoring the youngster's situation closely, with a view to luring him to Old Trafford.
Roberto Di Matteo also planned to lodge a rival bid to bring Bazoer to Stamford Bridge, but both Chelsea and Manchester United's efforts now look to have been in vain, after Ajax announced the capture of the highly-rated teenager.
Bazoer is believed to have signed a three-year contract with the Eredivisie giants, as under Dutch FA rules, clubs are not allowed to offer players under the age of 18, a deal longer than that period.
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