Born to Jewish parents in North Adams, Massachusetts, Melcher began his career as a song plugger while married to his first wife, singer Jane Rappaport in New York. He then worked as an agent and road manager for The Andrews Sisters and eventually married Patty Andrews on October 19, 1947. The couple divorced on March 30, 1950.

Slightly more than a year later, he married Doris Day, and they formed their own production company, Arwin Productions, in 1952. With the exception of one movie, all of his projects were starring vehicles for Day.

In 1962, Melcher made his only foray into Broadway theatre with The Perfect Setup, a play starring Gene Barry, Angie Dickinson, and Jan Sterling. It closed after five performances.

Melcher died on April 20, 1968. According to Day's 1975 autobiography, Melcher's physician informed her that Melcher suffered from an enlarged heart. Melcher practiced Christian Science and elected not to seek medical intervention until his condition deteriorated.

Shortly after Melcher's death, Day discovered that he had committed her to a CBS situation comedy, The Doris Day Show, without consulting her, and that not only had he lost the millions she had earned throughout their marriage because of poor Investments, but he had left her seriously in debt as well. She sued his Business partner Jerome B. Rosenthal and was awarded nearly US$23 million for fraud and malpractice following a 99-day trial. Rosenthal declared bankruptcy, and in August 1977 Day settled with his insurers for US$6 million that was paid in 23 annual installments.