Webster was born on Dec. 20, 1907, in New York, N.Y. He attended New York University and Cornell University and worked as a seaman and a dance instructor before breaking into show business with the lyrics to the song ‘Masquerade' (1931). He went on to write the words to ‘Two Cigarettes in the Dark' (1934) before going to Hollywood to work on the 1935 films ‘Under the Pampas Moon', ‘Dressed to Thrill', and ‘Our Little Girl'. In the late 1930s his lyrics often were performed in films by young soprano Bobby Breen.

Webster's songwriting benefited from several successful collaborations. He and Sammy Fain won Academy awards for ‘Secret Love' from ‘Calamity Jane' (1953) and ‘Love is a Many Splendored Thing', the title song of a 1955 film. They also worked together on title songs for ‘April Love' (1957), ‘A Certain Smile' (1958), and ‘Tender Is the Night' (1962). A fruitful partnership with Johnny Mandel produced the Oscar- and Grammy-winning song ‘The Shadow of Your Smile' from ‘The Sandpiper' (1965); the two teamed up the following year for ‘A Time for Love' from ‘An American Dream'. Webster also worked with composers Hoagy Carmichael, Duke Ellington, Henry Mancini, and others.

Webster's other songs for motion pictures included ‘Remember Me to Carolina' from ‘Minstrel Man' (1944), ‘Doctor, Lawyer, Indian Chief' from ‘The Stork Club' (1945), ‘The Loveliest Night of the Year' from ‘The Great Caruso' (1951), ‘The Green Leaves of Summer' from ‘The Alamo' (1960), and ‘Follow Me' from ‘Mutiny on the Bounty' (1962). He also added lyrics to the instrumental ‘Lara's Theme' from ‘Doctor Zhivago' (1965) to create ‘Somewhere My Love', which became one of the most popular songs of 1966.

Webster also contributed to the stage productions ‘Jump for Joy' (1941), ‘Alive and Kicking' (1950), and ‘Christine' (1960) and wrote the words for various television theme songs. He was inducted into the Songwriters' Hall of Fame in 1972. After battling Parkinson's disease for several years, he died on March 18, 1984.