John Costigan was a first cousin of the actor, dramatist, and producer George M. Cohan. When he was twelve years old his parents died, and he went to live with the Cohans. They brought him to New York in 1903 and got him a job with the H. C. Miner Lithography Company, which produced theater posters. Starting as a press boy, he worked his way up to designer. During the same period he spent five nights a week improving his skills with the Kit Kat Club, a group of illustrators and newspaper artists who met in a Fourteenth Street studio to draw from models. Costigan also studied drawing for a year at the Art Students League under George Bridgman.
He first exhibited in 1915 at the Macdowell Club in New York, but it was not until after World War I, during which he served in the Fifty-second Infantry Division in France, that his work began attracting notice. In 1920 Costigan won a Julius Hallgarten Prize in the Academy's annual exhibition and an Isidor Water Color Prize for a work in the Salmagundi Club's annual exhibition. His first one-man show was at the Rehn Galleries, New York, though he later became associated with the Babcock Galleries. He continued contributing to Academy annual exhibitions for some years, receiving a Saltus Medal for Merit in 1925, a Thomas B. Clarke Prize in the 1927 annual and a Benjamin Altman Prize in that year's winter exhibition, the Ellin P. Speyer Prize in 1928, and, in the annual of 1946, an honorable mention for a work in graphic media.
After he and the sculptress and professional artist's model Ida Blessin married in 1919, the couple settled in Orangeburg, New York, remaining there permanently. During the Great Depression, Costigan did magazine illustration and, like so many artists in the period, murals for public spaces under federal programs. Costigan painted post office murals in Girard, Ohio (1938); Rensselaer, Indiana (1939); and Stuart, Virginia (1942).
Costigan's mature work was as a landscapist. As early as 1916, he had begun taking sketching trips to Rockland County, New York. He took his motifs from the woods around his home in Orangeburg. Figures were always secondary to his concern with setting up patterns and rhythms in the features of his close-up perspective on nature. When he introduced figures into his pictures, his models were family members: his wife, his children, and, later, his grandchildren.