He started his career in popular music in the 1960s, writing lyrics for songs including "Sealed With A Kiss", "Save Your Heart for Me" and "Hurting Each Other".
Udell wrote the lyrics and co-wrote the book for the Broadway musicals Purlie (1970), Shenandoah (1975), Angel (1978), Comin' Uptown (1979) and Amen Corner (1983).
He received a Tony Award for Best Book of a Musical for Shenandoah, and was also nominated for Best Original Score.