Greaves' junior club was Renown United. Starting with the St George Dragons where he had been a local junior Greaves, like Brian James battled for recognition in the star-studded Dragons line-up who boasted a choice of centres with Reg Gasnier, Billy Smith and Johnny Riley in their squad. Nonetheless Greaves managed 23 first grade appearances in his two years at senior level with the club.
He shifted to Canterbury where he became a first-grade regular and from where he was chosen in 1966 for New South Wales and later that year to represent Australia in the two Tests of the domestic Ashes series against Great Britain.
He was a member of the Canterbury side who knocked St George out of the 1967 final thereby ending the Dragons' record breaking run but a week later suffered the igominy as the man left to chase down Bob McCarthy in the New South Wales Rugby Football League season 1967 Grand Final after Greave's was waiting on a pass from his hooker Col Brown which McCarthy intercepted and which would change the course of the game and decide the premiership.
He selected on the 1967 Kangaroo tour where he played in four Tests against Great Britain and France and in ten minor matches. He was a member of Australia's victorious 1968 World Cup squad.
Greaves captained Canterbury in 1970 and after leaving the club made his final representative appearance in 1973 from CRL Group 6 club Campbelltown City Kangaroos, when he turned out for Country Firsts. Greaves finished his career as captain- coach of the Campbelltown City Kangaroos, leading them to the 1973, 1974 & 1975 CRL Group 6 titles.
- "John Greaves". bulldogs.com.au. Canterbury-Bankstown Bulldogs. http://www.bulldogs.com.au/default.aspx?s=players. Retrieved 23 December 2013.