Eldad Tarmu was born in Los Angeles, California, where he started his musical career studying drums and percussion. He learned to play jazz vibraphone mentored by Dave Pike. He studied in Israel at Tel Aviv University, then he returned to the US and began touring internationally with various jazz ensembles, performing in festivals and music venues in over twenty-five countries, mainly in Europe and Asia. In 1997 he released his first record, Aluminum Forest, followed by Get Up Close in 2001, to notable critical acclaim.

Throughout his career, he collaborated with names like Ron Affif, Ray Anderson, Mike Clark, Billy Higgins, Freddie Hubbard, Taj Mahal, Frank Morgan, Poncho Sanchez, Cybill Shepherd, and Ernie Watts.

Upon graduating from California State University Los Angeles with a Master's degree in Afro-Latin Music in 2005, he was appointed Head of the Jazz Department at the "Richard Oschanitzky" Jazz School of Tibiscus University (currently a department of West University) in Timisoara, Romania, following a collaboration with Romanian bassist, violinist, and music researcher Johnny Bota, who was one of the school founders. During his residence, he established a partnership with the American Corner in Bucharest, aiming to promote jazz as an American art form, and toured Eastern Europe with various ensembles and guest jazz musicians from the US. In 2008, he returned to the US to continue his education at Stony Brook University, where he got a Master's degree in Classical Composition as well as a Doctor of Musical Arts degree in Jazz Performance, under the guidance of Ray Anderson. A professor of Music Studies at Hudson County Community College and Raritan Valley Community College in New Jersey, he developed and introduced a Latin-American Music course for HCCC,

In recent years, he has been increasingly focused on original contemporary classical music for chamber ensembles and vibraphone, composing for string quartets and woodwind quintets, as well as piano works. His second chamber music CD, called Stained Glass Stories, was released in 2017 under the musician's label, Queen of Bohemia Productions, and in 2018 under 4Tay Records. The album is dedicated to the musician's late mother, Chicago-born painter Galya Pillin-Tarmu.

An album of jazz-funk originals, called Tarmu Jazz Quartet, featuring saxophonist Adam Hutcheson, bassist Sam Bevan, and drummer Cengiz Baysal, was released in early 2023.

His latest project features Horace Silver compositions arranged for vibraphone, bass, and drums, and has been released in January 2025.

Eldad is endorsed by Zildjian and Mike Balter Mallets.