On the international level, he first appeared for the Argentine national team, winning the Copa América. Later in his career, he played for the Italian national team and took part in some of the 1962 World Cup. After his retirement as player, he coached several teams in Argentina, including the national side.
Sívori's footballing talent was acclaimed and he won the coveted European Footballer of the Year in 1961 and was later named by Pelé as one of the top 125 greatest living footballers in the FIFA 100 during 2004.
Especially while with Juventus, he was able to utilise his vision and passing skills, working in unison with Charles and Boniperti. Because of his playing style, country of birth and at times rebellious nature on and off the field, Sívori is retroactively compared to a player who emerged after him; Diego Maradona, with some parts of the media dubbing him "the Maradona of the Sixties".
Sívori was born in San Nicolás de los Arroyos, a town which falls within the Buenos Aires Province of Argentina. As a youngster Sívori became heavily interested in the game of football and by the time he reached his teens he was signed up to a side from his home province; River Plate. The teenage Sívori was given a chance to break through into a squad which included the likes of Ángel Labruna, Félix Loustau and Amadeo Carrizo. He soon earned the nickname El Cabezón (bighead) from the fans, due to his playing style.
River were able to win the Primera División Argentina in 1955, the title was confirmed when River beat hated local rivals Boca Juniors 2–1 at La Bombonera, in Buenos Aires, with just one game remaining. The same season River won the Copa Río de La Plata by beating Nacional from Uruguay. The following season he had similar success when River won the Argentine league title on the final day of the season; beating Rosario Central 4–0, with Sívori scoring the final goal. Sívori would play his final game for River against the same team on 5 May 1957.
During the 1957–58 season, the 21 year old Sívori was signed by Italian club Juventus after being spotted by Renato Cesarini. Juventus paid 10 million pesos (the equivalent of £91,000) for the transfer, which was a world-record transfer fee for the time. Sívori's move would prove bad for River's league fortunes, in the 18 years after 1957 they were unable to win the league in Argentina. However, they were able to complete their El Monumental stadium (previously nicknamed the horseshoe) by adding a fourth stand baring his name, with the money from the deal.
Prior to the arrival of Sívori and Welshman John Charles, Juventus had been going through somewhat of a slump. However, the duo along with experienced Juventini Giampiero Boniperti put together a formidable force and won Serie A during 1957-58. The good form continues and Sívori won two more scudetto titles (1959-60 and 1960-61) as well as two Coppa Italia's (1958-59 and 1959-60). Omar Sívori's hard work had paid off and he was named European Footballer of the Year (also known as Ballon d'or) in 1961.
The same year as his personal achievement however, "the Magical Trio" as they were known, had broken up with Boniperti's retirement and the following season John Charles moved back to Leeds United. Sívori stayed on with the Old Lady, notably scoring the only goal in a 1-0 victory against Real Madrid, making Juventus the first Italian side ever to win at the Santiago Bernabéu Stadium. Sívori did not win anymore championships or trophies with Juventus, and left after the 1964-65 season, because of a disagreement with new coach Heriberto Herrera.
With Juventus, Sívori scored 167 goals in 253 appearances in all competitions, remaining Juventus' fourth highest goalscorer ever as of 2007. He also holds the record for most Juventus goals in a single league game; during the 9-1 victory against Inter Milan on 10 June, 1961 he scored six goals, this is also the joint record for any Serie A team shared with Silvio Piola of Pro Vercelli.
He helped the team win the 1957 South American Championship held in Lima, Peru. Argentina dominated in every game during that year's Copa América, wins included an 8-2 victory against Colombia and a 3-0 victory against close rivals Brazil.
Following his move to Italy in 1957, Sívori was barred from playing for the Argentine national side by the country's government. Sívori himself had some Italian ancestry, hense his surname and in April 1961 he made his debut for th Italy national football team. In total Omar earned nine caps and scored eight goals while playing in azzurri.
|?.||18 March, 1956||Mexico City, Mexico||2-2||Draw||1956 Pan American Championship|
|?.||17 March, 1957||Lima, Peru||3-0||Win||1957 South American Championship|
|?.||28 March, 1957||Lima, Peru||6-2||Win||1957 South American Championship|
|?.||6 April, 1957||Lima, Peru||1-2||Loss||1957 South American Championship|
|1.||25 April, 1961||Bologna, Italy||3-2||Win||Friendly|
|2.||24 May, 1961||Rome, Italy||2-3||Loss||Friendly|
|3.||15 June, 1961||Florence, Italy||4-1||Win||Friendly|
|4.||4 November, 1961||Turin, Italy||6-0||Win||FIFA World Cup 1962 Qual.|
|5.||4 November, 1961||Turin, Italy||6-0||Win||FIFA World Cup 1962 Qual.|
|6.||4 November, 1961||Turin, Italy||6-0||Win||FIFA World Cup 1962 Qual.|
From 1972 until 1974, Sívori took charge of the Argentine national football team, he helped the club qualify for the 1974 FIFA World Cup. Sívori was the first man to call up Ubaldo Fillol for the national side, Fillol would become one of the most highly regarded keepers in Argentine history. After that he became a full-time scout for Juventus in South America. In March 2004, he was named by Pelé as one of the top 125 greatest living footballers and honoured as part of the in FIFA 100. The following year in February 2005, Sívori died in his hometown of San Nicolás, at the age of 69 due to pancreatic cancer.