Practicing architect, teacher of and author on Greek and Italian architecture. Anderson was born in Dundee, Scotland, to James Anderson, a tea dealer, and Margaret Steel (Anderson). In his early years he had limited access to artistic and architectural education. That which he did get was primarily through office routine and private reading. In 1877 he became an apprentice to the architect James Gillespie (1854-1914) of St. Andrews. He subsequently moved to an office in Dundee, and ultimately to Glasgow by 1888, where he worked as a draftsman with Thomas Lennox Watson (1850-1920).

Second director of the Courtauld Institute and scholar of the art of the Crusades. Boase was the son of Charles Millet Boase, a bleaching mill manager at near Dundee and Anne Malcolm Sherrer Ross. He attended Rugby School from 1912. A prize given for an essay on Lorenzo de' Medici led to a scholarship at Magdalen College, Oxford. At Oxford he studied under the historian Francis Fortescue Urquhart (1868-1934), known as "Sligger," whose method can be seen in Boase's own work.