Born in Andover, Massachusetts, to Dorcas (née Curley; 07 Jan 1915-12 Oct 1993) and Phillip Anthony Costello (07 Dec 1912-09 Jun 2000). He grew up in Andover with his brother Michael.
After graduating from Phillips Andover Academy in 1955, Anthony went to both the Rhode Island School of Design, and the University of Florence in Italy, then he attended Case Western Reserve University in Cleveland, Ohio, from which he received a master of fine arts degree.
Tony first tried painting as his artistic outlet, something he would continue on and off all of his life, but he also loved theater, and toured with the Cleveland Playhouse in 1961. He then appeared in Boston theater and finally on Broadway. In 1963, he moved to Hollywood, looking to work more in film and television.
In 1974, he started writing a story in which he could star when it was produced. The story became a miniseries, then a
novel, and when he was finished there was no part for him. Some studio producers showed interest, but when he said that the deal came with him as scriptwriter, they turned him down. Bantam Books published the story as a novel in early 1982 under the title Jericho. The book is a love story set around the Great Depression, the union movement, and the struggle between bosses in a Massachusetts mill town in decline in the 1930s.
Anthony Costello died at his home, after suffering from AIDS.