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Vuskovic will join Spurs on a contract running until 2030, the club said on Monday. British media reported the deal was worth around £12 million (US$14.64 million).
Under Fifa rules, Vuskovic must wait until he is 18 before he can arrive in England.
The centre back has played 11 times for Hajduk Split since making his senior debut in February, becoming the youngest player to feature in the Croatian top flight at 16 years and two days old.
Vuskovic also has five caps for Croatia’s under-17 team.
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