William Greer was born in was born in Preston on 28th February 1872. After playing local football he joined Preston North End in 1891. He made his debut the following year against Darwen and scored one of the goals in Preston's victory.

The following season he moved to right-half and was a member of the team that finished second to Sunderland in the 1892-93 season. The following season he played most of his games at centre-half. An injury in the 1896-97 forced him into retirement.

After the First World War Greer joined former Preston players, Bob Holmes, Jack Warner and John Morley in coaching Dick Kerr Ladies, the best woman's football team in England.

William Greer died in 1937.