He was born in Beverley in Western Australia to publican Edgar Tanner and Emily Prosser.
His family moved to Victoria and he attended All Saints Grammar School in St Kilda before becoming an accountant with the Commercial Bank of Australia.
During World War II, he served with the Royal Australian Air Force.
Tanner was a lightweight amateur boxing champion, and was a referee at the Olympic Games in Melbourne in 1956, Rome in 1960, Tokyo in 1964 and Mexico City in 1968, as well as at the Commonwealth Games in Perth in 1962 and Kingston, Jamaica, in 1966.
In 1967 he was elected to the Victorian Legislative Assembly as the Liberal member for Morwell, but he was defeated in 1970.