Born on a farm near Hubert, North Carolina, Henderson attended Wallace High School, Wallace, North Carolina, graduating in 1938. He earned an LL.B. degree from Davidson College in 1942 and graduated from University of North Carolina Law School in 1949 after serving in the United States Army Air Corps from 1942 to 1946.
He became a lawyer in private practice and served as assistant general counsel to the Committee on Education and Labor, United States House of Representatives from 1951 to 1952; as solicitor of Duplin County, North Carolina, General Court from 1954 to 1958; and as a Duplin County, North Carolina, judge from 1958 to 1960.
In the early 1980s he also ran a lawyer-lobbyist company Cook and Henderson with Republican Marlow Cook. Their major client was the Tobacco Institute.
Henderson was elected as a Democrat to the Eighty-seventh and to the seven succeeding Congresses (January 3, 1961 – January 3, 1977). He served as chair of the Committee on Post Office and Civil Service (Ninety-fourth Congress). He was not a candidate for reelection to the Ninety-fifth Congress in 1976, a seat won by a staff from his office, Charles Orville Whitley. Henderson died on January 13, 2004, in Wilmington, North Carolina, and was interred at Rockfish Cemetery, Wallace, North Carolina.