He was born as the son of a fisherman and a tailor; his parents' names were Christofis and Argyro. He grew up with ten other brothers and sisters. He started his footballing career in Büyükada (an island in Istanbul) but professionally played first with Taksim SK, a club based in the European sector Istanbul. Küçükandonyadis transferred to Fenerbahçe in 1947, achieving instant success. He was one of the first Turkish footballers to play abroad, playing during 1951–1953 for ACF Fiorentina in Italy and OGC Nice in France. Returning to Fenerbahçe, he won two Istanbul League titles and later, after the start of the Turkish national league, three Turkish League (1959, 1961 and 1964) championship titles. In the season 1953–1954, he was the top scorer in the Turkish league. Küçükandonyadis scored in all a total of 423 goals in 615 games for Fenerbahçe. After ending his career in Turkey in 1964, Küçükandonyadis played a single season in Greece with AEK Athens FC. He participated in five games in the 1965 season scoring two goals before an injury in the match against Iraklis forced his retirement.
Küçükandonyadis was capped 50 times for the Turkish national football team, 9 of which as the captain. He also played at the 1954 World Cup netting in 2 goals, one against West-Germany and the other against South-Korea. He scored 22 goals for the national team and was the top scorer for Turkey until overtaken by Hakan Şükür. He was the first Turkish football player to receive the "Golden Honor medal", from the Turkish Football Federation, for having played for the National Selection in 50 international matches.