He was a prominent Australian artist and was one of the founding members of the Heidelberg school. Born in Dorchester, Dorset, England, where his parents were newspaper editors, Roberts migrated with his family to Australia in 1869 to live with relatives. Settling in Collingwood, a suburb of Melbourne, Victoria, he worked as a photographer's assistant through the 1870s while studying art at night under Louis Buvelot and befriending others who were to become prominent artists, notably Frederick McCubbin. He returned to England for three years of full-time art study at the Royal Academy Schools from 1881 to 1884.
Through the 1880s and 1890s he worked in Victoria, in his studio at the famous studio complex of Grosvenor Chambers at 9 Collins Street in Melbourne, and at a number of artists' camps and visits around the colony. He married 35 year old Elizabeth (Lillie) Williamson in 1896, and they had a son, Caleb. Many of his most famous paintings come from this period. Roberts was an expert maker of picture frames, and during the period 1903–1914, when he painted relatively little, much of his income apparently came from this work.
He spent World War I in England assisting at a hospital. In Australia, he built a house at Kallista, near Melbourne. This was a particularly productive and happy period in Roberts' life.
Elizabeth died in January 1928, and Tom remarried, to Jean Boys, in August 1928. He died in 1931 of cancer in Kallista near Melbourne. He is buried near Longford, Tasmania.