William was the eldest son of Arthur Wheeler and Catherine Wheeler nee Helsham. Arthur and Catherine came to Australia from Ireland and arrived at Port Phillip on 31 March 1851 aboard the 'Anna'. They are buried at Longwood Cemetery. William's parents initially settled at Kilmore and this is where he was born. They later owned and leased 'Upton' Station and 'Wanghambeham' Station on which William grew up and worked. Arthur's brother Henry had married Catherine's sister Cecilia, and they too had come on the 'Anna' in 1851. Initially Arthur and Catherine had 'Upton' and Henry and Cecilia had 'Wanghambeham', but when due to illness Henry and his family returned to Ireland, Arthur first looked after both stations and after leaving 'Upton' just ran 'Wanghambeham'. In 1893 due to a number of issues, including a legal dispute Arthur was forced to sell his home of over 30 years at 'Wanghambeham'. Arthur, William and his sister Mary moved into smaller accommodation at Creighton's Creek and William began working as a drover and farm labourer. William married Mary Elward at Carlton on 15 September 1893.
William and Mary had six children:
Henry Helsham (Helsham) Wheeler 1893-1988
Mary Catherine (Kate) Wheeler 1896-1991
Ellen (Nellie) Wheeler 1899-1982
Cecilia (Ciss) Wheeler 1900-1989
William Wheeler 1902-1902
Nora Wheeler 1905-abt 2000