Coomaraswamy was born in Colombo in 1877 to Muthu Coomaraswamy, a Tamil lawyer and legislator, and to an English mother. His father died when he was very small and he was brought up in England. He took a doctorate in geology at the University of London and returned to Ceylon in 1903 to direct its mineralogical survey, in the course of which he identified the mineral thorianite.
The survey took him around the island, and what he saw of village craft changed the direction of his life. Mediaeval Sinhalese Art, printed in 1908 on his own press in the manner of William Morris, is an argument as much as a description: that the crafts he was recording were the surviving practice of a society in which making things had not been separated from religion, and that colonial rule and industrial production were ending it. He was active in the Ceylon national movement in the same years.
He moved to Indian art proper, publishing on Rajput painting and on the iconography of the dance of Shiva, and in 1917 he became the first keeper of Indian art at the Museum of Fine Arts in Boston, largely by giving it his own collection. He built the department over thirty years and remained there until he died in 1947.