Lyon confirmed that the initial fee will be £54 million with €10 million more in add-ons.
Tottenham's previous record deal was the £42 million they spent on defender Davinson Sanchez in 2017.
"We are delighted to announce the signing of Tanguy Ndombele," Tottenham said in a statement.
"The France international central midfielder has signed a contract with the Club until 2025."
Ndombele's arrival came just hours after Spurs made their first signing in 18 months by securing teenage winger Jack Clarke from Leeds.
However, securing Ndombele, a player coveted by a host of top clubs around Europe, is a sign of intent from Tottenham, who moved into a new 62 000 capacity stadium last season.
Spurs boss Mauricio Pochettino has challenged the club to match his ambition after reaching the Champions League final for the first time.
Ndombele, 22, starred as Lyon reached the last 16 of the Champions League last season and finished third in Ligue 1.