In 1881 he returned to New York and speedily achieved great success in portraiture, numbering among his sitters Oliver Wendell Holmes, John Burroughs, Walt Whitman, Henry G. Marquand, R. A. L. Stevenson, and president McCosh of Princeton University. His first exhibition in the Paris Salon of 1893 was a brilliant success and was followed by his immediate election to the Société Nationale des Beaux Arts. Many additional honors were bestowed on him. In 1901 he was named Chevalier of the Legion of Honor, and in 1902 he became a member of the National Academy of Design. He was a member of the American Academy of Arts and Letters. Among the gold medals received by him were those of the Paris Exposition (1900) and the World's Fair at St. Louis (1904).
Many examples of his paintings are on display in museums and public places in the United States and in Europe, including the Metropolitan Museum of Art, the Brooklyn Art Museum, the Los Angeles County Museum of Art, the Museum of Fine Arts, Boston, the Butler Institute, and the Library of Congress in Washington D.C. In addition, in the entrance hall to the Art Museum of the Carnegie Institute in Pittsburgh, a series of Alexander's murals entitled "Apotheosis of Pittsburgh" (1905-1907) covers the walls of the three-storey atrium area.
Alexander was married to Elizabeth Alexander Alexander, to whom he was introduced in part because of their shared last name. Elizabeth was the daughter of James Waddell Alexander, President of the Equitable Life Assurance Society at the time of the Hyde Ball scandal. The Alexanders had one child, the mathematician James Waddell Alexander II.
Alexander's original and highly individual art is based upon a very personal interpretation of humanity. He died in New York.