Born in Providence, Rhode Island to Irish-American parents on February 29, 1888, life never afforded Costigan the opportunity to pursue an academic education in art, but for a few weeks he studied under William Merritt Chase and George Bridgeman at the Arts Students League in New York City. This was the extent of his formal art instruction. Costigan did however find other means to hone his skills and experience the camaraderie of other artists, spending nights sketching live models at the Kit Kat Club, a studio on 14th Street that was a favorite haunt of newspaper artists and illustrators. Costigan had confidence that he could learn what he needed to learn from a rigorous discipline of self-teaching—that if he worked hard enough he could develop his own talent. By the time he was thirty years old, Costigan had exhibited at the Corcoran Gallery of Washington D.C., as well as the McDowell Club and Babcock Gallery, both of New York City. His career was well on its way when World War I came along and he enlisted in the army, serving in the 52nd “Pioneer” Infantry Division in France.
In 1928, his illustrious peers at the National Academy of Design brought Costigan into the fold—acknowledging him as their equal—by bestowing upon the artist the distinction of National Academician. This was (and remains) one of the highest honors to be accorded to an American artist. The fact that Costigan achieved the distinction of National Academician with no formal art education is a testament to his talent and work ethic.