Born in Ferrara, he was the sole legitimate son of Galeazzo I Visconti and Beatrice d'Este. In 1322 he was lord of Piacenza, but in the same year, together with his father, was forced to flee. In 1325 he took part in the victorious Battle of Altopascio against the Guelphs.

In 1329 he bought, for 60,000 (or 125,000) florins the title of imperial vicar of Milan by the emperor Louis IV in opposition to the Pope, who nominally held the right of the nomination. Azzone paid only 12,000 of the promised florins, the feeble Louis being unable to force the payment. In the same years he was named as one of the assassins of his uncle Marco Visconti, but was never convicted. On March 15, 1330 Azzone was appointed perpetual lord of Milan. The expiring of the excommunication pending over the family since the times of his grandfather Matteo.

In 1331, Charles of Bohemia, the son of King John of Bohemia and future emperor as Charles IV, was nearly poisoned to death at a banquet in Pavia. Azzone was again suspected. In the August of the same year he allied with Theodore I, Marquess of Montferrat, against King Robert of Anjou, in order to capture his possessions in north-western Italy. In 1332 he also conquered Bergamo and Pizzighettone, continuing in 1335 with Lodi, Crema and other Lombardy lands who had ceded themselves from the Papal States, as well as Vercelli and Cremona.

Lodrisio, who had escaped, set a company of mercenary troops with the help of the Scaligers of Verona, who sought vengeance for Azzone's support to Venice during the war with Verona. The latter was however defeated by the Milanese troops in the battle of Parabiago, to which Azzone, suffering of gout, did not partake. Lodrisio was imprisoned in the castle of San Colombano al Lambro.

He died in 1339 of a gout attack, and was buried in the church of San Gottardo, which he had commissioned some years before. He had no male heirs, having had only a daughter. He is also remembered for his great construction works in Milan and other city of Lombardy.