Broschi was born in Apulia, Kingdom of Naples, the son of Salvatore Broschi, a composer and chapelmaster of the Cathedral of the Puglinese citizens, and Caterina Berrese (according to the Book of Baptisms of the Church of S. Nicola, today near the Episcopal Archives).
The Broschi family moved to Naples at the end of 1711, and enrolled Riccardo, their firstborn, in the Conservatory of S. Maria di Loreto, where he would study to become a composer under G. Perugino and F. Mancinipresso.
Next, he moved to London in 1726 and stayed there until 1734 and wrote six heroic operas, his most successful being Artaserse.
In 1737 he moved to Stuttgart and briefly served at the Stuttgart court (1736-7) for Charles Alexander, Duke of Württemberg, then returned to Naples before joining his brother in Madrid in 1739.
The dramatic relationship between the Broschi brothers is the quintessence of the movie Farinelli (1994), in which a few of his works are performed.