The 19-year-old, who had also been linked with Manchester United, Barcelona and Paris-St Germain, led the Dutch giants to the Champions League semi-finals last season.
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After arriving by private jet, the defender said: "I am happy to be here."
He made his debut in 2016 and has won the Eredivisie and Dutch Cup, and was a Europa League finalist in 2017.
De Ligt scored eight goals in 77 league appearances for the Amsterdam club, who he joined at the age of nine, and became the club's youngest captain in March 2018.
He scored the winning goal against Juve to send Ajax through to the Champions League semi-finals, where they lost to Tottenham.
De Ligt made his debut for the Netherlands in March 2017, despite having started just two league games for Ajax at the time.