The 22-year-old Sinner will compete at an Olympics for the first time on the clay courts of Roland Garros where he made the semi-finals of the French Open last week.
Sinner has claimed three titles in 2024, his maiden Grand Slam at the Australian Open, Rotterdam and Miami.
Sinner, 30th-ranked Musetti, Matteo Arnaldi, the world number 34, and 41st-ranked Luciano Darderi will play singles in Paris.
In doubles, the Sinner-Musetti pairing will be joined by French Open runners-up Andrea Vavassori and Simone Bolelli.
The Italian women's team features French Open finalist and seventh-ranked Jasmine Paolini, 43rd-ranked Elisabetta Cocciaretto and world number 68 Lucia Bronzetti.
Paolini and Sara Errani will play doubles after the duo made the women's final at Roland Garros last week.