Born Raymond Brost in Buffalo, New York, Henderson moved to New York City and became a popular composer in Tin Pan Alley. He was one third of a successful songwriting and music publishing team with Lew Brown and Buddy De Sylva from 1925 through 1930, responsible for several editions of the revue called George White's Scandals and such book musicals as Good News, Hold Everything!, and Follow Thru. After De Sylva's departure, Henderson continued to write with Brown through 1933, then worked with other partners. In 1934 he composed the musical Say When with lyricist Ted Koehler.
Henderson's biggest hit songs included "That Old Gang of Mine", "Annabelle" (both 1923), "Bye Bye Blackbird", "Five Foot Two, Eyes of Blue", "I'm Sitting on Top of the World" (all 1925), "The Birth of the Blues" (1926), "The Varsity Drag" (1927), "You're The Cream In My Coffee" (1928), "Button Up Your Overcoat", "You Are My Lucky Star" "I'm A Dreamer, Aren't We All", "Keep Your Sunny Side Up" (1929), "The Thrill Is Gone", and "Life Is Just a Bowl of Cherries" (1931).
