He was the son of Tommaso Ristori, the leader of an opera troupe belonging to the King of Poland and Elector of Saxony August II the Strong (based in Dresden).
August II lent his opera troupe to the Russian Empress Anna for the celebration of her coronation in Moscow.
It was given under his, and his father's direction, with thirteen actors and nine singers including Ludovica Seyfried, Margherita Ermini and Rosalia Fantasia, in 1731 in Moscow.
In 1916 the German musicologist Curt Rudolf Mengelberg published the first study on Ristori and his music: Curt Rudolf Mengelberg, Giovanni Alberto Ristori: ein Beitrag zur Geschichte italienischer Kunstherrschaft in Deutschland im 18.
Although short on biographical details, it is a landmark publication because Mengelberg had access to many Dresden music sources now missing.