Slot will succeed Jurgen Klopp, who has stepped down as Liverpool manager after nine years in charge.
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"It is certainly not an easy decision to close the door behind you at a club where you have experienced so many wonderful moments and worked successfully with so many wonderful people," Slot told Feyenoord's club website.
"But as a sportsman, an opportunity to become a head coach in the Premier League, at one of the biggest clubs in the world, is difficult to ignore."