Rotch was born in Milton, Massachusetts to Benjamin Smith Rotch (1817-1882) and Annie Bigelow Lawrence (1820-1893). He studied humanities at Harvard College for four years, graduating in 1871, spent two years (1872-1873) at MIT, then from 1874-1880 studied at the École des Beaux-Arts and in the atelier of Emile Vaudremer.
While in France he was in charge of the restoration of the Château de Chenonceau.
In 1880, he became partner of Rotch & Tilden (Boston) with George Thomas Tilden, designing churches, the Memorial Library in Bridgewater, Massachusetts, gymnasiums of Bowdoin College and Phillips Exeter Academy, various buildings of Milton Academy, the art schools and art museum of Wellesley College, and many private houses and business blocks throughout the United States. In 1893, he designed Ventfort Hall in Lenox, Massachusetts for George Hale Morgan and Sarah Morgan, the daughter of Junius Spencer Morgan.
Rotch was chairman of the visiting committee of Fine Arts of Harvard University, a member of the Corporation of the Massachusetts Institute of Technology, and with his brother and sisters founded the Rotch Traveling Scholarship which sends an American student of architecture for a minimum of eight months study and travel abroad.
On November 16, 1892, he married Lisette DeWolf Colt.
In his will, he left more than $100,000 (equivalent to $2,768,077 today) to public and charitable organizations.
- Castle, William Richards; Pier, Arthur Stanwood (1895). The Harvard Graduates' Magazine. Harvard Graduates' Magazine Association. Retrieved 5 March 2017.
- Lawrence, Robert Means (1904). The Descendants of Major Samuel Lawrence of Groton, Massachusetts: With Some Mention of Allied Families. Printed at the Riverside Press. Retrieved 5 March 2017.
- Brooke, James (19 August 2001). "TRAVEL ADVISORY; Berkshires Mansion Preserves the Gilded Age". The New York Times. Retrieved 4 March 2017.
- "BOSTON INSTITUTIONS REMEMBERED.; Two Men Leave Large Sums of Money for Their Endowment.". The New York Times. 23 August 1894. Retrieved 5 March 2017.
- Wilson, James Grant; Fiske, John, eds. (1900). "Rotch, Arthur". Appletons' Cyclopædia of American Biography. New York: D. Appleton.
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