Vasiliou was born on August 4, 1938 in Nikaia. He started his A' Division career at Apollon Athens before transferring in the summer of 1965 to AEK for 1,500,000 drachmas - a record for both clubs at that time. With AEK, he won the league title in 1968 and the Cup in 1966.
His career ended abruptly in 1969 allegedly after interference by junta-appointed Secretary General of Sports, Costas Aslanidis, himself. Vasiliou played a few more years for Ionikos in the lower divisions before quitting altogether.
After his playing days were over, he became a successful food-stuffs merchant.