Jennings was born in Kilgore, Texas. He attended school just outside Tyler, Texas, in the nearby Chapel Hill Independent School District. In 1967, Jennings earned his B.A. from Stephen F. Austin State University, located in Nacogdoches, Texas. He then taught at the University of Wisconsin–Eau Claire for three years.
Throughout his career, Jennings has written for a wide variety of artists including Steve Winwood, Eric Clapton, B.B. King, Joe Sample, Rodney Crowell, Mariah Carey, Jimmy Buffett, Barry Manilow and Roy Orbison.
With Steve Winwood, Jennings wrote a series of albums including, Arc of a Diver, Talking Back to the Night and Back in the High Life, an album which contained the hits "Higher Love", "The Finer Things", and "Back in the High Life Again". Winwood won the Record Of The Year and Outstanding Male Vocal Performance. Both Jennings and Winwood were nominated for the Song of the Year award for "Higher Love."
With Joe Sample, Jennings wrote "Street Life" (a world-wide hit for the Crusaders with singer Randy Crawford) and several songs for various albums by the Crusaders for guest vocalists, including Joe Cocker ("I'm So Glad I'm Standing Here Today"), and Bill Withers ("Soul Shadows").