Having studied composition with Broadstock and Conyngham at the University of Melbourne, Stuart Greenbaum holds a position at the Melbourne Conservatorium of Music as Professor, having also served as Head of Composition from 2007 to 2023. He is the author of over 235 works including 26 sonatas, 8 string quartets, 5 piano trios, 7 concertos, 6 symphonies and 2 operas. Stuart Greenbaum is published by Wise Music G. Schirmer Australia.

Greenbaum’s music is heard regularly in Australia and abroad. Nelson, a 3–act opera with libretto by Ross Baglin, was presented in London in 2005 and premiered in full at the 2007 Castlemaine State Festival. Their second opera, The Parrot Factory, received a 5-show season in 2010 staged by Victorian Opera at The Malthouse. Major choral works include The Foundling (1997) and Brought to Light - Symphony No.5 (2022), commissioned by Cantori New York. From the Beginning was commissioned for the sesquicentenary of the Royal Melbourne Philharmonic in 2003 and The Sydney Philharmonia Choirs commissioned The Night that the Museum Burned for their 2022 season.

Greenbaum’s orchestral output includes works for the SSO, MSO, AYO, ACO and CSO.
City Lights a Mile Up was commissioned by the Tasmanian Symphony orchestra. Major chamber works have been written for The Australia Ensemble, Southern Cross Soloists, Omega Ensemble, Grigoryan Brothers, Ensemble Liaison, Ensemble Francaix and The Australian Ballet.

He was Featured Composer at the 2006 Aurora Festival, resident composer at the 2009 Port Fairy Spring Music Festival and Composer in Focus at the 2009 Bangalow Music Festival. In 2009 he was Australia's representative for the Trans-Tasman Composer Exchange, working in Auckland with NZTrio on a new piano trio,
The Year Without a Summer, which toured nationally for Chamber Music New Zealand, in Sydney for the ISCM World New Music Days (2010) and internationally at the City of London Festival (2011). He was Featured Composer with the Flinders Quartet in 2016 and Resident Composer with MYO in 2019. He was a Resident Fellow at the Akiyoshidai International Art Village in Japan in 2019 and again in 2023, and Composer in Residence at the Visby International Centre for Composers in Sweden in 2020. The epic solo piano work, Ice Man, received its North American premiere through Amir Farid at New York’s Carnegie Hall in 2024.

Prizes include the Dorian Le Galliene Composition Award, the Heinz Harant Prize, and the Albert H. Maggs Composition Award.
90 Minutes Circling the Earth won Orchestral Work of the Year at the 2008 Classical Music Awards.