Rami Kleinstein was born in New York. He moved to Israel with his family in 1970. As a child, he studied piano and classical music. In 1988, he married the Israeli singer Rita. They performed together in the 1980s while serving in the military. Kleinstein subsequently composed and produced many of Rita's songs. The couple, now divorced, has two daughters.
In 1986, Rami's first solo album ביום של הפצצה (meaning On the day of the bomb) achieved gold status. In 1997, his sixth album, כל מה שתרצי (meaning Everything you want) reached triple platinum status within ten days of release. He was voted "Singer of the Year" in 1995, after his album תפוחים ותמרים (meaning Apples and dates) reached triple platinum.