[2] The nickname followed Angelillo when he, along with fellow national team forwards Omar Sívori and Humberto Maschio, moved from Argentina to play football in Italy after the tournament.

When the club appointed Helenio Herrera as the team's new manager, Angelillo's independent nature, rebellious character, and hedonistic lifestyle off the pitch led to several disagreements between the two; as a result, Angelillo was sold to Roma during the 1961–62 season, for 270 million lire, in spite of offers in Argentina from his former club, Boca Juniors.

[5][6][3] From 1961 to 1965, Angelillo played 106 games with Roma in Serie A, scoring 27 times, winning the 1960–61 Inter-Cities Fairs Cup, and the 1963–64 Coppa Italia with the club.

The following year, he signed with Lecco, playing 12 matches and scoring one goal, with the team being relegated to Serie B at the end of the season.

Wanting to return to first division football, he subsequently had a trial with Napoli, before agreeing to return to Milan as a reserve; he only made three appearances, scoring one goal, winning the 1967–68 Serie A title with the club, although he did not appear in Milan's victorious 1967–68 European Cup Winners' Cup campaign that season.

[3][11] After moving to Italy and acquiring Italian citizenship through his grandfather, Angelillo later appeared for the Italy national team, making his debut in a 2–1 away defeat to Austria on 10 December 1960, although, in spite of the presence of several foreign-born Italian players – including his compatriots and former teammates Sívori and Maschio –, he was left out of the Italian squad for the World Cup in Chile two years later; in total he made two appearances for Italy between 1960 and 1962, scoring 1 goal, which came in his second and final appearance – a 6–0 home victory over Israel, held in Turin, on 4 November 1961.

Prior to his marriage, while playing for Inter during the 1960–61 season, he had a much publicised affair with the dancer Attilia Tironi – whose stage name was Ilya Lopez – whom he had met in a nightclub.