The eldest son of Hugh Rose of Birse, Aberdeenshire, he was educated at Marischal College, Aberdeen.
He then moved to Kew, and in 1758 to Chiswick, where he conducted a successful school until his death, 4 July 1786.
Among Rose's pupils was Charles Burney the younger, who married his daughter Sarah.
Among his friends was Bishop Lowth, and his executors were Thomas Cadell and William Strahan, the publishers.
Rose, Millar and Strahan were all born and educated in Scotland but pursued their careers in London.