Israels grew up in a musical family. His stepfather, the singer Mordecai Bauman, often collaborated with the composer Hanns Eisler and hosted artists such as Paul Robeson, Pete Seeger and The Weavers. In 1948, Israels was introduced to jazz at a concert by Louis Armstrong’s All Stars, organised by his parents.
A self-taught bassist, he later studied music at Brandeis University and in Paris, where he undertook his first professional work with Bud Powell. He made his first recording in 1958 with Cecil Taylor and subsequently worked with Eric Dolphy, Stan Getz and Coleman Hawkins, amongst others. He gained international renown as the bassist of the Bill Evans Trio (1961–1966), where he succeeded Scott LaFaro.
Later, he led the National Jazz Ensemble and collaborated with, amongst others, the Kronos Quartet, Rosemary Clooney and the Metropole Orchestra. From 1986 to 2010, he was head of the Jazz Studies department at Western Washington University.