Brevoort took up the study of architecture in 1850, under his cousin, James Renwick, Sr.; he received a certificate in architecture from New York University in 1854. He is said to have been a student of Thomas Seir Cummings at the Academy school in the same period. However, his name is not recorded in the Academy school register for the single season in this period, 1851-52, that Cummings had charge of the school, nor at any other time. Cummings did take over the school again in 1856 and remained its principal to 1865, but by that time Brevoort was established as a professional. That he had studied under Cummings was noted in the summary of his life entered into Academy minutes in 1919, so it is likely Brevoort was a private pupil of Cummings. Brevoort's life-long and exclusive choice of landscape as subject matter further suggests that the Academy school's concentration on drawing the figure might have been of no interest to him.
Brevoort clearly looked to the Academy to establish his reputation, and made himself an active and welcome colleague in its membership. He was first represented in its annual exhibition in 1856, and except for the period in the 1870s when he was abroad, he was liberally represented in every annual thereafter through 1902, and made a final contribution to the Winter Exhibition the year before his death. He was the Academy school's lecturer on perspective from 1869 through the 1871-72 season; he served on Council from 1870 to 1872.
His first wife died; in 1873 he married Marie Louise Bascom who had been an Academy student from autumn 1869 through the 1871-72 season. Brevoort auctioned the works then accumulated in his studio and took his bride to Europe; by 1874 they were settled in Florence, where they remained for the next seven years. He again delivered lectures on perspective at the Academy in 1882-83 season, and lectured on painting and sculpture in 1899-1900. He also delivered special lectures in the Academy on the influence of French art, given January 18, 1892, and on science and art, given January 9, 1893. In these last years of the century, the school's regular lecturer on perspective was Frederick Dielman; Brevoort is recorded as a school lecturer on "sculpture and painting" in these years. Considering the subjects of his special lectures, it is likely these school lectures were more general discussions of his experience and point of view, than technical instruction.
In the early years of his career, Brevoort had located his studio in the vital center of the New York art community, the Tenth Street Studio Building, where he was addressed 1858 to 1862; through the remainder of the 1860s and early '70s (and probably the duration of his first marriage) he kept a studio on lower Fifth Avenue. On his return from Europe he established his studio on East Twenty-third Street, in the immediate neighborhood of the the Academy, where he remained into 1902--two years longer than the Academy's headquarters survived there--when he retired to the home he had built in Yonkers in 1890. Apparently it was an active retirement: he helped found the Yonkers Art Association and exhibited in its first three shows, 1916 through 1918. This renewal of professional activity was probably the spur to his late reappearance in an Academy exhibition.
That Brevoort was at the time one of the few surviving Academicians elected in the earlier nineteenth century was noted by the Council's January 7, 1918 direction that "letters of congratulation [be sent to] Messrs. Brevoort, Griswold, Hennessy, and John F. Weir." On January 11 Brevoort replied to the corresponding secretary, Harry Watrous, "I have now reached my 85 1/2 year and am glad to say that I can 'put in' from four to five hours of work nearly every day--also I would like to thank the hanging committee for placing my picture in so conspicuous and excellent a place in the present exhibition. I being one of the old ones did not know exactly how it might be received."