Tchouameni has signed a six-year contract with the newly crowned European champions.
The 22-year-old is Real Madrid's second summer signing following the free transfer of Antonio Rudiger from Chelsea to the Santiago Bernabeu.
Tchouameni was being chased by the likes of Chelsea, Paris Saint Germain and Liverpool but has settled on Carlo Ancelotti's side.
He comes into a Real Madrid midfield that despite their recent European triumph is ageing with Luka Modric, Toni Kroos and Casemiro all into their thirties.
Tchouameni is set to be part of the next dominant midfield trio in the Spanish capital alongside compatriot Eduardo Camavinga and Federico Valverde.
The France international joined Monaco from Bordeaux in January 2020 and made 50 appearances across all competitions last season, scoring four goals.
Tchouameni becomes Real Madrid's fourth-most expensive signing of all-time after Eden Hazard, Gareth Bale and Cristiano Ronaldo.
Tchouameni was part of the France side that won the UEFA Nations League last year, and has won 11 caps for Les Bleus.
Tchouameni will be formally presented as a Real Madrid player on Tuesday.
