Paris Saint-Germain forward Mbappe, 24, accepted the proposal after discussions with coach Didier Deschamps earlier in the day.
Tottenham goalkeeper Lloris brought an end to his international career in January after losing the World Cup final a month earlier.
Lloris, 36, had been skipper for more than a decade. Atletico Madrid attacker Antoine Griezmann was named vice-captain after Manchester United centre-back Raphael Varane also hung up his boots following the defeat to Argentina in December.
Mbappe, who has played 66 times for his country, had been heavily linked with the role for weeks and scored a hat-trick in the World Cup final loss after helping Les Bleus to the title in 2018.
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