Tipped as one of the pre-tournament favourites on home soil, France reached the gold medal match at the Games earlier this month, only to suffer a gut-wrenching 5-3 loss to Spain after extra time.
Henry's side dramatically fought back from 3-1 down to level the contest at 3-3, but two extra-time efforts from Spain forward Sergio Camello propelled La Roja to Olympic glory.
Nevertheless, a silver still represented France's best finish at the men's football tournament since 1984 - when they won gold - and just their third podium finish overall after also finishing second in 1900.
Henry was due to remain in charge of France's Under-21s until the conclusion of next year's European Championships, but on Monday afternoon, the French Football Federation confirmed that the 47-year-old had left his post for "reasons of his own".
Speaking to the FFF website, Henry labelled the 2024 Olympic silver one of the greatest moments of his life and reflected on a "magical" time in charge, saying: "I would like to thank the FFF and President Philippe Diallo, who offered me this incredible opportunity.
France chief 'regrets' Henry decision after Olympic medal
"Winning the silver medal at the Olympic Games for my country will remain one of the greatest prides of my life. I am incredibly grateful to the Federation, the players, the staff and the supporters who allowed me to live a magical experience."
Meanwhile, FFF president Diallo admitted that he 'regretted' Henry's decision to leave his post after witnessing the 47-year-old's "rigour" and "love" for the France shirt, adding: "On behalf of the FFF, I would like to thank Thierry Henry for all the work he has accomplished at the head of the Espoirs and Olympiques teams.
"We obviously regret this decision because Thierry Henry was able to achieve the objectives that had been set for him by winning a silver medal at the Paris Olympics, 40 years after the Olympic medal in Los Angeles.
"Having followed him throughout this campaign, I was able to discover his great professionalism, his rigour and his love of the blue jersey. We wish him good luck for the rest of his career."
Henry has also managed Monaco and Montreal during his managerial career, as well as serving as assistant to Roberto Martinez with the Belgium team at Euro 2020 and the 2022 World Cup.
The all-time leading scorer for Arsenal, Henry led France to three wins from their opening four Euro 2025 qualifying games, as they sit second in Group H behind Slovenia, who have played a game more.