János Göröcs started his football career as a player with Jutagyár in 1949. After a move to Vasas Izzó, Göröcs was by then a Hungarian youth international. At the age of 18, he moved to Újpest, where he became a key player for a decade and a half. He became a full international in 1958 and his finest moment came two years later when he was a member of the 1960 Tokyo Olympics bronze medal-winning team. Two years later in Chile, Hungary finished fifth at the FIFA World Cup. Göröcs ended his playing career in the early seventies playing for Tatabánya.
As a coach, Göröcs returned to Újpest working first as a junior coach, and later as the head coach of the senior team in the second half of the 1980s, guiding them to the Hungarian Cup in 1987. He worked in Kuwait and Iran in the 1990s. In 1985, Göröcs was made an “honorary champion” of Dózsa Újpest, and in 2008 was made an honorary citizen of the city of Újpest. He received a similar honour in Budapest in 2012. Göröcs graduated from the College of Police and served as a Major of the Police.
Hungary