Cordella studied in Naples with Fedele Fenaroli and Giovanni Paisiello.
[1][2] In 1804 he composed his first work, a cantata entitled La Vittoria dell'Arca contro Gerico.
[1][3] With the help of Paisiello in 1805 he had the possibility to produce in Venice his first opera, Il ciarlatano, which was appreciated for its comic verve[1] and then performed in other cities in northern Italy, including Milan, Turin and Padua.
[1][2] Cordella continued his activity mainly in Naples, where he was appreciated for his opere buffe, while his few opere serie met with failures.
His greatest success was Una follia,[2] first performed in 1813, an opera buffa featuring "a vivacious plot and a melody that flows agreeably".