The deal for Ndombele, who has agreed a six-year contract, could eventually be worth £62.7 million, according to the French club.
Spurs said in a statement on Twitter: “We are delighted to announce the signing of Tanguy Ndombele from Olympique Lyonnais.
“The France international central midfielder has signed a contract with the club until 2025.”
Watch him above being put through his paces in Lyon training: