Eyran Katsenelenbogen was born in Israel on July 5, 1965; no source specifies a birth city. As a child he studied under Aida Barenboim, the mother and first teacher of pianist and conductor Daniel Barenboim. He went on to train at the New England Conservatory of Music in Boston under an unusually prestigious lineup of teachers — Ran Blake, Paul Bley, Fred Hersch, Danilo Pérez, George Russell and Gunther Schuller — and has taught at NEC's Preparatory School and School of Continuing Education since 1996, including work developing techniques for teaching improvisation to students with special needs and diverse abilities.

His most notable teaching connection is pianist Matt Savage, an autistic musician whose career gained national television exposure; Katsenelenbogen was Savage's first piano teacher, and the two recorded a joint album, One Is Not Fun, But 20 Is Plenty, in 2000. His own recorded catalogue runs from an early-1990s Jerusalem-recorded release through I'ts Reigning Kats & Dogs & Bogen (2002), Solotude (2005), 88 Fingers (2009) and Outstandards (2019); it has been reviewed across three decades by AllAboutJazz, Jazz Journal and Jazz Police. He has performed at Iridium Jazz Club in New York, the Teatro di Marcello in Rome, the Tel Aviv Jazz & Blues Festival, Jordan Hall in Boston and the Glenn Gould Studio in Toronto. In 2009 he premiered a crossover arrangement of Mussorgsky's Pictures at an Exhibition with Andrei Ivanovitch at Jordan Hall, and in 2014 he co-headlined a "Piano Fight" concert tour of China with fellow Israeli pianist Tal Zilber. He has been a member of the Recording Academy since 2020, and per one source is a descendant of the 16th-century rabbinic scholar Meir Katzenellenbogen, with reported distant family ties to Felix Mendelssohn and Martin Buber.

Katsenelenbogen's training runs through an unusually wide spread of jazz pianism — Ran Blake's Third Stream sensibility, Paul Bley's free-leaning lyricism, and George Russell's theoretical rigor among his named teachers — and his own catalogue reflects that range, moving between original compositions and standards repertoire (his 2019 album is titled, simply, Outstandards). His three-decade teaching post at NEC, including specialized work with students of diverse abilities, sits alongside the performing career as a genuinely central part of his musical identity, most visibly in his early mentorship of Matt Savage.