The contract is for four years, Real Madrid says on its website.
Konaté's contract with the English giants expired at the end of the season, meaning he will leave on a free transfer.
The Madrid club has previously completed the signings of midfielder Bernardo Silva from Manchester City and defender Marc Cucurella from Chelsea.
French World Cup defender Konaté was on the bench when France played its opening match against Senegal on Tuesday evening (3–1).
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