Geoffrey Saba was born in Toowoomba, Queensland, into a family of Lebanese descent. He exhibited significant early musical tendencies despite the lack of any musical tradition in his family, and began to study the piano with Audrey Askin at the age of seven years. During his final two years in Toowoomba he studied with Mary Childe. In 1963 he was awarded the University of Queensland Music Scholarship for that year, and elected to continue his studies in 1964 at Melbourne University's Conservatorium of Music, where his teacher was the distinguished ABC associate artist Raymond Lambert. At the end of that year he commenced study with Ada Corder, and he remained working with her until his departure to study overseas. In 1967 he was awarded the first Australian Musicians' Overseas Scholarship, and he performed Australian contemporary music at the 1968 Adelaide Festival of Arts before leaving Australia in October that year for study in London.

He worked with Maria Curcio and Peter Feuchtwanger initially in London, and then with Vlado Perlemuter in Paris, and Stefan Askenase. He made his London début in 1972 at Wigmore Hall to much critical acclaim, and premiered in that programme a work specially written for the occasion by the Brisbane composer Colin Brumby. In the following years he invited several Australian and British composers to write for him. In 1974 he was awarded a bronze medal at the First Arthur Rubinstein International Piano Master Competition, and he began to concertize internationally throughout Eastern and Western Europe, the Middle East, India, Japan, North America and South East Asia, incorporating regular return visits to his native Australia.

He continues to perform new music, and his large repertoire includes much rarely-performed music from the early part of the 20th century. In the late 1970's he met the scholar and one of Musica Viva's founding fathers, W A Dullo, after one of his Sydney concerts, who presented him with his completions of unfinished Schubert Piano Sonatas, and these have become central to his performing repertoire as he considers them prime examples of Australian musicological research. More recently, he has given the Asian premiere of Peter Sculthorpe's Piano Concerto, a work which he continues to promote.
He is regularly invited to give master classes when on tour, and in Australia, where he appears at most of the Schools of Music. He has played at festivals in Great Britain, South East Asia and Australia. Geoffrey's best-selling recordings for Carlton Classics have achieved tremendous critical acclaim. His annual London solo recitals since 2001 are recorded and released by Carnegie Concerts, and his discography to 2011 comprises fourteen releases, with repertoire from Bach to Bartok, including the complete Debussy Preludes and Beethoven's Diabelli Variations. His recent Mozart recording elicited these remarks from the reviewer in Limelight: "This is real classical playing of a kind rarely encountered now. Saba's playing of Mozart's great Rondo K511 can stand comparison with that of Artur Schnabel ... one of his great strengths is his controlled rhythm throughout ... his performances are refreshingly free from the personalised distortions that have crept into Mozart playing ... ". Geoffrey Crankshaw wrote in Musical Opinion: "Geoffrey Saba is an artist of perception. What we have here is a Diabelli perfectly blending gravity and humour. In the Opus 126 Bagatelles he offers wit and brilliance and succeeds admirably. An excellent disc." Following his March 2011 all-Schubert Perth recital, Neville Cohn wrote in The West Australian " I cannot recall ever before listening in Perth to the massive Sonata in D D850. It is excruciatingly difficult music to bring off successfully but Saba gave us an enthralling reading, a performance that focussed unerringly on minute, finely articulated detail without for a moment losing sight of the grand sweep of the work. Saba is a master tone-colourist and he employs that gift to the maximum: dandelion-delicate pianissimi cheek by jowl with massive fanfare-like climaxes that astonished the ears ... Rather like those steam cleaning machines that are used to get rid of accumulated grime on old buildings to allow them to be seen in their original, pristine glory, Saba's intense musicality enabled him to offer Schubert's much-loved Moments Musicaux in a way that made one feel as if these exquisite miniatures, too, were being heard as the composer had wished them to be played."

The International Franz Schubert Institute, Vienna, has published his essay on a performer's approach to playing Schubert's unfinished piano sonatas in its facsimile edition of the C major Sonata (Relique) D 840. For the past two years he has been artistic director of the annual Easter Spring Festival at Ellys Manor House, Lincolnshire. He is a member of the Advisory Board of the Australian Music Foundation and is committed to mentoring young Australian artists as part of the Foundation's work.