Galanos attended Bridgeton High School in Bridgeton, New Jersey, and went on to graduate from Traphagen School of Fashion in New York in 1943. He worked for fashion designers in Paris and New York City, including Hattie Carnegie and film costume designer Jean Louis. He opened Galanos Originals in Los Angeles in 1951.
Galanos won a host of awards during his career, including the Coty Fashion Award in both 1954 and 1956, as well as being inducted into the Coty Hall of Fame in 1959. He received the Council of Fashion Designers of America Lifetime Achievement Award in 1985. In the year 2000, the City of New York began honoring American fashion designers by placing bronze plaques along the pavement of 7th Avenue. Dubbed the "Fashion Walk of Fame", Galanos was one of the first designers to be so honored.
Though he officially retired in 1998, Galanos continues to make his presence known in the fashion world. In 2002, he blasted the fashion industry for catering to only young women with perfect bodies. In an interview with WWD Magazine, he said "How many women can wear just a patch over their crotch and a bra?" he asked over lunch at the Pierre, shaking his head in contempt. "Aren't you embarrassed when you see a young girl walking down the street practically naked?"
Galanos is the uncle of fine jewelry designer Diana Vincent, of Washington Crossing, PA.