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 W. Hughes, later settled at Mount Pleasant.
[1] 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.
He was a director of Elder, Smith & Co., Ltd., 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.
He was married, leaving a widow, Gwendoline Grace Melrose (1908–1991).