The move is now subject to the player agreeing personal terms.
The 23-year-old centre-back, who has represented the Netherlands at under-21 level, will travel to Wales for negotiations in the coming week.
Swansea will go into the 2016-17 campaign under new backers, having been taken over by an American consortium.
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Swansea City have agreed a deal with Dutch giants Ajax to sign defender Mike van der Hoorn, BBC Wales Sport has learned.