Perrine's father, a homesteader and trader, died early, leaving the family with no means of support. In his adolescence, Perrine worked as a farm hand and carpenter. He moved to New York City (c. 1893) and studied at the Cooper Institute and at the National Academy (1894-95, 1896-97). During his student days at the National Academy he began painting in Ridgefield, New Jersey, on the property of the illustrator James E. Maxfield. The landscape work he did there impressed his fellow students, and soon a number of them were working with him in Ridgefield. The Country Sketch Club, an outgrowth of these plein-air sessions, held a number of exhibitions including ones at the National Academy (c.1899) and at the Art Institute of Chicago (1901). National Academy members who exhibited in these shows include: Walter Farndon, Charles Hawthorne, Jonas Lie, G. Glenn Newell, David E. Roth and Maurice Sterne.
Perrine roomed with Maurice Sterne in New York City and then after 1902 Perrine lived at the foot of the Palisades in various abandoned buildings where he was able to paint directly from nature. His first one man exhibition was held at Glaenzer's (1903); he also exhibited at Durand-Ruel, the New Gallery, and in the Armory Show. In 1911 he married Theodora Snow, a musician.
After 1912 Perrine became involved with lumia, a procedure where he would paint from colored light which was projected on a screen. After World War I, Perrine moved to Millburn, NJ. He taught Saturday morning art classes to children, and an exhibition of the work of these children was held at the Grand Central Art Galleries (1934). He published Let the Child Draw in 1936. In the 1950s he and his wife taught at the Buxton School in Williamstown, Massachusetts. He lived the last few years of his life in New Canaan, Connecticut.