[1] Stuart Greenbaum grew up in Melbourne, his mother a trained classical pianist who taught music at Deakin University.

[4][5][6] The early 1990s saw Greenbaum producing a number of pieces for stage, including a time as the resident composer at the Playbox Theatre in Melbourne.

[9] Greenbaum's work 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.

In 2007 he was commissioned by the artistic director of the Southern Cross Soloists to compose a work, Mondrian Interiors, featuring Marshall McGuire.

[12][13] In May 2024, Iranian-born Melbourne pianist, Amir Farid, gave the US premiere of Greenbaum’s half hour piano sonata Ice Man (1993) to a sell-out audience at Carnegie Hall.