Born in Rosewell, Scotland, he played 162 games for Heart of Midlothian F.C. from 1966 to 1973, before moving to Aberdeen F.C. and playing a further 91 games with them. After a brief stint with the San Antonio Thunder of the NASL, he moved to Australia and Sydney City in 1977 for the inaugural National Soccer League season. During his time at Hearts he also played for the Scottish u-23 side.
It was at this time he retired from playing and immediately became the full-time coach of Sydney City, winning a further two national championships in 1981 and 1982. After Sydney City withdrew from the NSL in 1987 he took charge of Sydney Olympic, guiding them to a grand final in 1989 before leaving early in the next season to take charge of the Australia national team. His national coaching career did not start there however.
He became coach of Australia B in 1984 before becoming assistant coach of the Socceroos in 1985. After taking over as Socceroos manager, he guided the team to some impressive friendly results against Sweden and the USA before coming close to qualifying for USA 94, only losing 1–0 as a result of a freak deflection to an Argentine side who had recalled Diego Maradona after some disappointing qualification results. He was also coach of the Australian Olympic football team at the same time.
In 1992, after defeating the Netherlands in a memorable encounter to qualify for the 1992 Summer Olympics, the team came within one game of the gold medal match, losing 6–1 to Poland before losing 1–0 to Ghana in the bronze medal playoff. In 1994, after allegations of inappropriate involvement in player transfers, an inquiry, chaired by retired New South Wales judge Donald Stewart, was set up to investigate these claims. The report published recommended his sacking, but he stayed on in the end.
Shortly after guiding the Olympic side through the 1996 Summer Olympics in which Australia failed to get past the group stage, Eddie resigned to take charge of Japanese side Sanfrecce Hiroshima. During his time there, a number of Australians, such as Aurelio Vidmar, Graham Arnold and Steve Corica played there. He returned to Australia in 2000 and shortly afterwards, he was diagnosed with Non-Hodgkin lymphoma, which he died of in 2003.