Browne attended public school in Salem, Massachusetts and then took up his study of art in Boston under Frank Benson and Edmund Tarbell at the school of the Museum of Fine Arts, and under Joseph de Camp and Ernest L. Major at the Cowles Art School. He then went abroad in about 1895, where he studied at the Acad‚mie Julian in Paris with Jules LeFebvre and Tony Robert-Fleury. He sent his first works to the Paris Salon in 1900. The next year he made his first trip to Holland where he was much influenced by the works of Rembrandt and Vermeer.
Upon Browne's return to the United States, he took a studio in the Sherwood Building in New York and and began summering in Provincetown, Massachusetts, where he established a summer school which became one of the principle attractions of that artists' colony. In winters Browne taught at the Grand Central Art School in New York. As inveterate a traveler as teacher, he regularly took classes abroad with him throughout the 1920s. In the last years of his life he again devoted himself to art education, accepting a post at the Mary Washington College of the University of Virginia, Fredericksburg, in 1944.
Browne was a frequent exhibitor and active in several of the major artists organizations in New York: The Salmagundi Club, which awarded him its Inness Prize in 190l, and several other prizes in later years, elected him its president in 1935 and 1936. He served the Allied Artists of America as president from 1930 to 1937, and was awarded its gold medal of honor in 1928 and again in 1934. The Academy awarded him a Hallgarten prize in 1928, and Altman prize in 1934; he served on the Council from 1933 to 1936.
Yet he maintained strong ties with France. His Bait Sellers of Cape Cod had been purchased by the French government from the Salon of 1904, and in 1925 the government again purchased one of his paintings and made him an Officer de l'Instruction Publique et des Beaux Arts. They honored him again in 1936 when he was made Chevalier of the Legion of Honor.
The first major exhibitions of Browne's work had been held at Knoedler's Gallery in 1910 and 1913; throughout the 1930s exhibitions of his work were held regularly at Grand Central Art Galleries.
Browne's early works, painted when he was a student in France, show an influence of the Barbizon school, especially Millet and Corot, in subject and style. During this period he did works depicting the landscape of French farm life, including but not featuring workers. He also did marines, often dramatic night scenes including ships. After his returned to America, his style became looser and his landscape tended to be unpopulated. Critics of his day termed his landscapes naturalistic or picturesque. The subject matter for his landscapes was taken from regular trips to southern France, Spain, the Barbary coast and, at home, from Provincetown.