Griesbach was born in Fort Qu'Appelle, North-West Territories, the son of Henry Arthur Griesbach, a North-West Mounted Police officer. In 1883, Henry was transferred to command Fort Saskatchewan; the family travelled on the Canadian Pacific Railway to Calgary and then by wagon train to Edmonton and Fort Saskatchewan, on occasion having to build or repair bridges in order to cross rivers. William Griesbach left the rest of the family in 1891 in order to attend St. John's College in Winnipeg, from which he graduated in 1895. Upon graduating, he returned to Edmonton and worked in a law firm for two years and in the Imperial Bank for one year, before returning to Fort Saskatchewan to work in a milling business for six months. He returned to Edmonton to study law.
Griesbach enlisted with the Canadian Mounted Rifles in 1899 to fight in the Second Boer War. He knew from being weighed in at boxing tournaments that he fell short of the minimum weight to enlist, so on his way to being weighed he surreptitiously grabbed a large piece of coal from the enlistment centre's coal box and held it behind his back while he stood on the scales. During his service, he was awarded the Queen's South Africa Medal and received four bars. Upon his return in 1901, he opened a law office of his own. An Edmonton Bulletin article in 1927 quoted him as saying of these early years
Pre-war political career
Griesbach's first bid for political office took place in the 1903 Edmonton election, when he made an unsuccessful bid for election to Edmonton Town Council, placing fourth of nine candidates in an election in which the top three were elected. He was more successful in the 1904 election when he was elected to a one-year term as an alderman to Edmonton's first city council placing eighth of seventeen candidates. He was re-elected to a two-year term in 1905, finishing first of ten candidates. That same year, he ran as a Conservative in the riding of Edmonton in Alberta's first provincial election. He was defeated by LiberalCharles Cross, and continued his service on city council. Griesbach resigned as alderman one year into his term in order to run for mayor in the 1906 election. He was victorious, collecting more than sixty percent of the vote in a three-person race and becoming, at twenty-eight years old, the youngest mayor in the city's history, before or since. He served a one-year term, but did not seek re-election and stayed out of municipal politics thereafter. He ran as a Conservative in the 1911 federal election, finishing second of three candidates in the riding of Edmonton. Griesbach's final involvement in provincial politics would come during the 1913 election, when he ran as a Conservative in Edmonton. He finished fourth of five candidates.
Griesbach was an accomplished cyclist and played ice hockey and soccer for Edmonton teams. He was a member of the Masonic Order, the Oddfellows, the Edmonton Veteran Association, the Canadian Club, and the Northern Alberta Pioneer and Old Timers' Association. In 1906, he married Janet Scott McDonald Lauder. William Antrobus Griesbach died in Edmonton on January 21, 1945, of a sudden heart attack. CFB Griesbach, the Griesbach Garrison, , and Edmonton's Griesbach neighbourhood are named in his honour. Mount Griesbach in the Victoria Cross Ranges of Jasper National Park is also named in his honor.