Varela's international debut came in a 3-2 win against Chile in the 1939 Copa America in Lima, Peru. Varela entered the match as a substitute.
He played 45 international matches for Uruguay from 1939 to 1954, in which he scored nine goals.
He's most remembered as the captain of the Uruguay team that won 1950 FIFA World Cup, in which he played a vital role. The decisive match was against the hosts Brazil. Uruguay needed to win, but Brazil could win the Cup with a draw. Then when the team were on the dressing room, Juan López, the coach of the Uruguayan team told his players that the best way they could get a chance against Brazil was if they adopted a defensive style, then he left the room and Varela told his teammates 'Juan is a good man, but if we do defend ourselves then we will suffer the same fate of Sweden and Spain' (they lost by a large margin against Brazil), and then said 'the game is played on the pitch, when you come out to the pitch, don't look to the crowd, those on the outside are of wood'. The speech played a vital role on his teammates, who played without fear getting a 0-0 draw on the halftime. 5 minutes in the second half, Brazil scored, and Varela took scene, when he intentionally walked slowly to his goal, picked up the ball and then argue with the English referee George Reader about an innexistent offside, with the intention of delaying the restart of the game so the crowd cooled off. After that he said to his teammates 'Now it's time to win' and the Brazilians in the crowd were in a silent mood. Uruguay scored with a goal of Schiaffino and then, 9 minutes before the finish, with a very nervous Brazil team, Alcides Ghiggia scored the 2-1 for Uruguay, winning the world cup.
He also played on the 1954 FIFA World Cup with Uruguay defending his 1950 title, but this time, Varela got injured before the semifinals against Hungary, Uruguay lost 4-2 at extra time. When Varela was present, Uruguay never lost a World Cup game.
His last match was on June 19, 1955 with Peñarol against América. Varela, one of the team's coaches along with Roque Maspoli, came off the bench for the second half but when he realized he couldn't continue, he decided to end his career.