Madrid announced Wednesday that Mendy will sign a six-year contract, with Lyon saying the transfer was worth 48 million euros ($54 million).
Mendy's signing comes a week after Madrid also acquired Belgium star Eden Hazard from Chelsea for a reported fee of 100 million euros and forward Luka Jovic from Eintracht Frankfurt for a reported 60 million euros.
The 24-year-old Mendy joined Lyon from Le Harve in 2017. He scored three goals in 44 appearances for Lyon last season, and made his international debut for France in a friendly against Uruguay in November.
Mendy will provide competition for Marcelo, who like many of his teammates underperformed last season when Madrid failed to compete for any major trophy.
Earlier this year Madrid also signed Brazilian defender Eder Militao, who will join from Porto next season. Teenage forward Rodrygo, bought from Brazilian club Santos for nearly 45 million euros ($50.6 million) last year, also will be added to the squad for next season.