Veira started his professional career in 1963 with San Lorenzo, in 1964 he became the topscorer in the Argentina Primera División at the age of only 18.

In 1967 Veira received his first call up to the Argentina national football team and in 1968 he helped San Lorenzo to win the Metropolitano championship without losing a game, to become the first team in the professional era of Argentine football to become unbeaten champions.

In his later career he played for Club Atlético Banfield in Argentina, Sevilla in Spain, Corinthians in Brazil, CSD Comunicaciones in Guatemala and Universidad de Chile.

Veira started his managerial career with San Lorenzo in 1980, he then had a short stint in charge of Vélez Sársfield before joining River Plate in 1985.

Veira has always maintained his innocence, and claimed that the boy was instructed by his mother to make the allegations for financial gains.