Valcareggi was born in Trieste. He had a successful playing career, playing for teams such as Fiorentina, Bologna, and his home-town club Triestina, ending his career in 1953. He won the Coppa Alta Italia with Bologna in 1946.
Valcareggi is also remembered for devising the infamous "staffetta" (relay) match strategy during the 1970 World Cup. Due to his focus on defensive stability, as well as the presence of two pure, prolific goalscoring strikers, Riva and Boninsegna, Valcareggi felt that it would not be possible to field Italy's two most revered advanced playmakers at the time, Gianni Rivera, and Sandro Mazzola, alongside each other. He believed the two creative players to be incompatible with each other, due to the rivalry between their respective clubs, and as he felt that deploying both players alongside the forwards would offset the balance within the starting line-up, in particular as Rivera, unlike Mazzola, was not renowned for his athleticism or defensive work-rate. He therefore conceived the plan, which essentially consisted of Mazzola playing the first half of each match, whilst Rivera would play the second half. Despite Italy's victory at the 1968 European Championship and their second place finish at the 1970 World Cup, the tactic was widely criticised by the media, in particular due to Italy's negative performance during the group-stage and in the final defeat to Brazil, despite demonstrating their ability to successfully apply a more offensive, exciting style of play with Rivera in the semi-final against West Germany. The two players only played together briefly in the final, when Rivera came on for Boninsegna for the last six minutes of the match.
Valcareggi also helped Italy to qualify for the 1974 FIFA World Cup, although they were knocked out in the first round of the tournament, which led to Valcareggi stepping down from his position as Italy's head coach; during the tournament, he had an infamous falling out with Giorgio Chinaglia, who insulted Valcareggi upon being substituted. Following his international career, Valcareggi worked as a club coach in Italy and also briefly served as a pundit, also working for Fiorentina's technical sector; he was inducted into the Fiorentina Hall of Fame in 2013.
Valcareggi died in Florence on 2 November 2005, at the age of 86.