Jenő Várady competed for the Pannónia Rowing Club, and later the Hungária Rowing Club. In 1908, at the London Olympics, he was the stroke of the Hungarian eights that finished fifth. In 1909 he moved to England and rowed for the Vesta Rowing Club, where one of his team-mates was the 1908 single sculls champion Harry Blackstaffe. In 1913, Várady returned to Hungary, where he again competed for Pannónia. In 1914, as a 52nd Infantry soldier, he received a Medal of Merit. After the war, he settled in Freiburg, Germany.