French sports daily L'Equipe reported that Mbappe had accepted the captaincy after speaking with coach Didier Deschamps.
"Kylian Mbappe is the new captain of Les Bleus. Antoine Griezmann is the vice-captain," French TV channel TF1 quoted Deschamps as saying in an interview to be aired on Sunday.
"Kylian meets all the requirements to have this responsibility. On the field as in the life of the group, by being a unifying element."
Mbappe had been touted as one of the candidates for the role since goalkeeper Lloris retired from international football in January, weeks after leading France to a second straight World Cup final, where they were beaten by Argentina.
Mbappe has been capped 66 times and played a key role in their successful 2018 World Cup campaign as well as their runners-up finish in 2022.