He was the left halfback of the Uruguay national team that won the 1950 World Cup tournament, after defeating Brazil in the decisive match.

He was the nephew of another Uruguayan international player, José Leandro Andrade, who was also a World Cup winner, having played for the Uruguay squad that won the first ever edition in 1930.

Born in the Barrio Sur of Montevideo, Víctor Rodríguez came to the world into a family that proudly revered the name of his uncle, José Leandro Andrade.

[3] At the 1950 World Cup in Brazil, Rodríguez Andrade, who at 23 years old was one of the younger members of the Uruguayan squad, played in all four of his team's matches.

In the final round match against the hosts, which would decide the winner of the tournament, his defensive duties included the marking of Zizinho, a task he was successful at until the beginning of the second half, when the Brazilian assisted Friaça, who scored the 1–0.

Uruguay, which had won its last South American title in 1942 when Rodríguez Andrade was in his teens, was unable to win it six straight times from 1945 to 1955, including the first two in which he appeared, 1953 and 1955.

Rodríguez Andrade died in May 1985, and a month after his death, Senator Luis Hierro Gambardella dedicated a speech to him during a session of the Congress.

The stamp featured the images of three of the most emblematic figures of the history of the club: in the center, Víctor Rodríguez Andrade, accompanied by his teammate Luis Rijo, and his coach Juan López.