The 37-year-old is planning to play in the singles and doubles at what will be his fifth Games.
“Arrived in Paris for my last ever tennis tournament,” Murray wrote on X.
“Competing for Team GB has been by far the most memorable weeks of my career and I’m extremely proud to get to do it one final time!”
The Scot’s first Games appearance was in Beijing in 2008, when he lost in straight sets to Lu Yen-hsun in the first round.
Four years later, Murray swiftly put the disappointment of a Wimbledon final defeat by Roger Federer behind him, defeating the Swiss in straight sets at London 2012 to win gold.
The Briton became the first male tennis player to win two Olympic singles titles when he beat Argentina’s Juan Martin del Potro at Rio 2016.
“Sir Andy has lived and breathed the values of tennis throughout his long career, championing equality and helping to send the message that our sport is for everyone,” International Tennis Federation president David Haggerty said.
“Sir Andy’s love of tennis will see him continue to be involved in helping to grow and develop our sport globally.”
The three-time Grand Slam winner had career-saving hip surgery in January 2019.
Murray, a two-time Wimbledon champion, played competitively at SW19 for one last time earlier this month when he was knocked out of the doubles in the first round alongside his brother Jamie.
A back injury had threatened Murray’s participation at Wimbledon and he left it until the final moment before pulling out of the singles. He had hoped to play mixed doubles with Emma Raducanu, but she pulled out of that planned pairing because of a wrist injury concern.
Speaking after his defeat at Wimbledon, Murray said: “It is hard because I want to keep playing, but I can’t.
“Physically it’s too tough now. I want to play forever. I love the sport.”
The Scot said earlier this year that he was “not planning to play much beyond the summer” but hoped to compete in Paris.
Dan Evans, the British number three, will partner Murray in the doubles.
The opening rounds of the tennis in Paris begin at Roland Garros on 27 July and the event concludes on 4 August, with medal rounds being played from 2 August.