The deal for Ndombele, who has agreed a six-year contract, could eventually be worth 70 million euros (£62.77million), 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."
Earlier, Tottenham also completed the signing of winger Jack Clarke from Leeds on a four-year contract for an undisclosed fee.
The 18-year-old will return to Elland Road on loan for the duration of the 2019-20 campaign.
Clarke had become the first signing made by Mauricio Pochettino's Champions League finalists since Lucas Moura joined from Paris St Germain during January 2018.
While Clarke is set to be one for the future, Ndombele can expect to be integrated straight into Pochettino's squad next season.
The midfielder started his professional career at Amiens in Ligue 2, before initially joining Lyon on loan during August 2017, the move becoming permanent the following summer.
Ndombele, 22, made 96 appearances in total for the Ligue 1 side and was handed his senior international debut for France during October 2018, and has so far been capped six times.
Lyon said in a statement: "Olympique Lyonnais thanks Tanguy Ndombele for his involvement with the club since his arrival in 2017 and congratulates him for his professionalism and performance."
Clarke, meanwhile, only made his senior debut in October but impressed enough to be named Leeds' young player of the season.
Marcelo Bielsa's side reached the Sky Bet Championship play-off semi-finals, where they were beaten by Derby.
Clarke made 25 appearances in all competitions for the West Yorkshire club, 20 as a substitute, and scored twice.
"Last season was my first at senior level, so I wasn't really expecting to come in and play as much as I did, but it was good for me just to get used to professional football," Clarke told Spurs TV.
"Obviously (Mauricio) is one of the best coaches in the world, a top, top manager.
"Hopefully he can help me push on and progress myself. I just want to carry on from where I left off at Leeds, kick on even more and then hopefully (following his loan) make an impact big enough to be in and around the (Spurs) team."