Robert was educated at Prince Alfred College, then settled on the family property "Rosebank", of 5,800 acres (2,300 ha) at Mount Pleasant, where he was a very successful breeder of Aberdeen Angus cattle and Merino sheep, and was involved in extensive tree planting.
Melrose"s parents George Melrose (22 December 1806 – 8 April 1894) and Euphemia, née Thomson, (died 1887) left Balerno, Scotland, on the Palmyra, arriving in 1839. George established a sheep run at Macclesfield with (later Sir) Walter West. Hughes, later settled at Mount Pleasant. He was chairman of the Anti-Cancer Campaign at the Adelaide University and on the board of the Adelaide Botanic Garden.
He was a keen golfer.
They had no children.
He was a director of Elder, Smith & Company, Limited., and from 1917 until his death was a longtime member of the Stockowners" Association and the Agricultural and Horticultural Society and its president 1919–1920. Melrose was a member of the Legislative Council from 1921 to 1927. Robert T. Melrose was a second generation member of a large and influential South Australian family founded by George Melrose.
