The 29-year-old Varane, who won the World Cup in 2018, scored five goals in 93 appearances for his country after making his debut in 2013.
The last of his caps was in the 2022 World Cup final in Qatar, in which France were beaten by Argentina on penalties.
“Representing our great country for a decade has been one of the greatest honours of my life,” said Varane.
“Every time I wore this very special blue jersey I felt immense pride. The duty to give it all, play my heart out and win every time we put on the field.
“I’ve been contemplating this for several months and deciding it’s the right time for me to retire internationally.”
Varane, who signed for United from Real Madrid in August 2021, has become the latest Les Bleus player to retire after the World Cup.
In January, Tottenham goalkeeper and captain Hugo Lloris stepped down three weeks after the final they lost to Leo Messi-inspired Argentine team.
Varane had been expected to take over the French captaincy from Lloris but Mbappe who won the FIFA Golden Ball award for netting eight times is expected to be made France captain.
Real Madrid Karim Benzema who was ruled out of the FIFA biggest competition in Qatar due to injury also retired from international duties shortly after his country’s loss to Argentina.
Mbappe is the current assistant captain in star-studded PSG and the 24-year-old could lead Didier Deschamps’ side on the pitch for his standout performance.
Mbappe named PSG’s new vice-captain
Kylian Mbappé, a French superstar, has been formally announced as the new team’s vice-captain by Paris Saint-Germain.
This was verified on Monday by the club’s manager, Christophe Galtier, following PSG’s 7-0 Coupe de France victory over Pays de Cassel.
Mbappe scored five goals as they thrashed the sixth-tier team at RC Lens’ Stade Bollaert Delelis while wearing the captain’s armband in Marquinhos’ absence.
Galtier raved about the 24-year-performance old’s as the Frenchman.
“Kylian scores goals. He is obviously fixated on scoring.
“He scored a good number of goals last year, like 56 or something. He and Neymar playing the entire game here was crucial, according to Galtier.