Salmons joined Sheffield United as a schoolboy and made his league debut at West Bromwich Albion on 30 September 1967. It took him a couple of years to win a regular place in midfield, and he was a member of the side that regained First Division status for the club in season 1970-71.
With 199 first team games behind him, Geoff moved on to Stoke City in a £200,000 deal in 1974. He made a brief return to the Blades on loan in September 1977, and soon after that he was transferred to Leicester City. In 1978, Chesterfield paid £35,000 for his transfer.