A six-time domestic champion of the Soviet Union with Dynamo Kyiv, Rudakov also helped Dynamo win the Soviet Cup twice, the Cup Winners' Cup and the UEFA Super Cup. He also represented the USSR national football team and helped them reach the finals of Euro 1972 finals. After the UEFA Euro 1972 along with his teammates by Soviet Union national football team — Revaz Dzodzuashvili and Murtaz Khurtsilava — he was included in the team of the tournament, along with such great players as Franz Beckenbauer, Gerd Müller, Paul Breitner, Uli Hoeness and Günter Netzer. In 1971 Rudakov was also chosen the Soviet Footballer of the Year and the best goalkeeper of the USSR in 1969, 1971, and 1972.