Born in Mount Morris, Illinois, Regan attended the public schools and Vincennes (Indiana) University. Regan served as a flyer in the United States Army Signal Corps during World War I. In 1920, Regan was involved in the real estate business and as an oil operator in Pecos, Texas. He served on the Pecos City Council and as mayor of Pecos 1929-1932. He served in the Texas Senate from 1933 to 1937. During World War II, he served as an intelligence officer in the Air Corps and was discharged with the rank of captain. He moved to Midland, Texas, and continued oil operations.
Regan was elected as a Democrat to the Eightieth Congress to fill the vacancy caused by the resignation of Robert Ewing Thomason. He was reelected to the Eighty-first, Eighty-second, and Eighty-third Congresses, and served from August 23, 1947, to January 3, 1955. Regan was an unsuccessful candidate for renomination in 1954 to the Eighty-fourth Congress. Regan served as the representative of Texas railroads in Washington, D.C.. He died in Santa Fe, New Mexico, on August 15, 1959. He was interred in Resthaven Memorial Park, Midland, Texas.