The son of Edward John Maxwell, a lumber dealer in Montreal, by his marriage to Johanna MacBean, Maxwell graduated from the High School of Montreal at the age of fourteen and was apprenticed to the firm of Shepley, Rutan and Coolidge in Boston.
Maxwell returned home to Montreal to supervise its construction, helped by having good relations with influential members of the Board.
In 1892, the jeweller Henry Birks hired Maxwell to design a new store in Montreal's Phillips Square.
In 1899, he designed a country house for Louis-Joseph Forget at Senneville, Quebec, a good example of his domestic work.
[1] In 1902, he went into partnership with his younger brother, William Sutherland Maxwell, who had studied at the École des beaux-arts in Paris.