The Federation Francaise de Football (FFF) said in a statement that Henry had cited personal reasons for his decision to end his contract which had been due to run to June 2025.
Henry, who won the 1998 World Cup as a player with France and is his country's second all-time leading scorer, earned plaudits after his team's performances at the Olympics.
"I would like to thank the FFF and President Philippe Diallo for giving me this incredible opportunity," said Henry, 47, in an FFF statement.
"Winning an Olympic silver medal for my country will remain one of the proudest moments of my life. I'm incredibly grateful to the federation, the players, the staff and the fans for giving me this magical experience."
Federation boss Diallo thanked the 1998 World Cup winner for "all the work he accomplished as coach of the Espoirs (under-21s) and Olympic sides".
"We obviously regret this decision, as Thierry Henry was able to achieve the objectives set for him by winning a silver medal at the Olympic Games in Paris," he added.
"Having followed him throughout this campaign, I witnessed first-hand his great professionalism, his rigour and his love for the blue jersey."