The Spanish champions said Tuesday that the transfer cost 25 million euros ($27.7 million).
In his debut for the national team, the 22-year-old Umtiti helped France reach the final of the European Championship, which it lost to Portugal on Sunday.
Umtiti played 170 matches for Lyon, scoring five goals in five seasons.
Able to play as a central defender or at left back, he will help strengthen a backline that saw Dani Alves and Marc Bartra leave since the end of last season.
Umtiti will undergo a routine medical exam before signing his contract on Friday.
He is Barcelona’s second reinforcement after it bought back attacking midfielder Denis Suarez from Villarreal.