The transfer is confirmed by Manchester City on the English club's website.
The midfielder started all three group-stage matches for the Netherlands at this summer's World Cup - including the 5-1 win against Sweden - but was benched when the team went out in the round of 16 against Morocco after a penalty shootout.
In total, Reijnders made 50 appearances and scored seven goals in a Manchester City shirt after joining from Italian club Milan last summer.
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