Altafini began his career in Italy with AC Milan in 1958, following the World Cup in Sweden; his talent and offensive potential had been noticed by Milan's agents during some friendly matches in Italy against Inter and Fiorentina in preparation for the upcoming tournament, in which Altafini scored. He was purchased by the Italian club prior to the World Cup in Sweden for 135 million Lire. Altafini made his scoreless Milan debut on 21 September 1958, at the age of 20, and, in his first season, he played 32 games and scored 28 goals, winning the 1958–59 Serie A title along the way, and demonstrating his goalscoring prowess; he also managed 4 goals in 4 Coppa Italia appearances that season, finishing the season with a total of 32 goals in 36 appearances in all competitions. His first league goal came on 5 October in a win against Bari. Altafini was the top scorer of the 1960–61 Coppa Italia, with 4 goals, although Milan were not able to make it past the second round of the competition. On 27 March 1960, he scored four goals in the Milan derby against local rivals Inter, which ended in a 5–3 victory for Milan. During these next few seasons, Milan managed a third and second-place finish, as Altafini continued to reach the 20 goal season mark. On 12 November 1961, he also managed four goals against Juventus, as Milan went on to win the Serie A title again during the 1961–62 season, in which Altafini finished as the league's joint top scorer with 22 goals in 33 games, alongside Aurelio Milani.