At eighteen, he studied at New York's Hunter College and later on at the Manhatan School of Music. At nineteen, he released his first album for Columbia Records and began an extended run performing at the Algonquin's Oak Room, followed a year later by his second album. He wrote the score and sang several songs for Rob Reiner's "When Harry Met Sally..." (1989), the soundtrack for which went multi-platinum. So far, while bringing back swing and big band music, he has earned one gold, four platinum and three multi-platinum albums, plus two Grammies.

His film acting debut was as B-17 tail-gunner Clay Busby in "Memphis Belle" (1990). He played mass-murderer Daryll Lee Cullum in the Sigourney Weaver and Holly Hunter film "Copycat" (1995) and Captain Jimmy Wilder ("Let's kick the tires and light the fires, big daddy!") in "Independence Day" (1996). Harry lives in Connecticut, is married to the former model Jill Goodacre, and has three daughters, Georgia Tatom, Sara Kate and Charlotte.