Țiriac was born in Transylvania, which is probably the reason why he has the nickname 'Count Dracula'. He first appeared on the international sports scene as a child ping pong champion, then subsequently as an ice hockey player on the Romanian national team at the 1964 Winter Olympics. Shortly after that he switched to tennis as his main sport. With fellow Romanian Ilie Năstase he won the men's doubles in the 1970 French Open and reached the Davis Cup finals several times in the 1970s.