Agnew was born in New York City, the son of William Agnew and Elizabeth Thompson Agnew; his ancestors, Huguenot, Irish and Scotch, came to America from time to time during the 18th century.[1] He entered the Columbia College in 1845 and graduated from there in 1849 with the degree of A.B.[1] He then received the degree of M.D. from the New York College of Physicians and Surgeons in 1852.[2] In 1856, he married Mary Nash, daughter of Lora Nash, a New York merchant.[1]
Agnew began to practice medicine in 1854[1] and became house surgeon, and later curator, at the New York Hospital.[2] He went to Europe for special study in his profession, and on his return was appointed surgeon to the New York Eye and Ear Infirmary,[2] from 1855 through 1864.
After the war, he assisted in establishing the Columbia School of Mines in 1864.[1] In the same year, he was also one of the founders of the New York Ophthalmological Society.[1] He was instrumental, in 1868, in the founding of an ophthalmic clinic in the College of Physicians and Surgeons, of which he was in 1869 appointed professor and lecturer.[2] He then founded the Brooklyn Eye and Ear Hospital in 1868 and the Manhattan Eye and Ear Hospital in 1869.[2]
In 1869 he was elected to the clinical professorship of diseases of the eye and ear in the College of Physicians and Surgeons, a position which he held till his death on April 18, 1888, in New York City.[1]
A part of the success of the United States Sanitary Commission must be attributed to Dr. Agnew's labors.[1] He prepared many papers relating to the eye and ear, and published in the current medical journals, also, a Series of American Clinical Lectures (1875), edited by E. C. Sequin (M.D.), besides numerous brief monographs.[2]