On the day that O'Malley was born, his father, Donogh O'Malley, an Engineer, was elected to Dáil Éireann for the first time. Donogh O'Malley served as a TD for Limerick East from 1954 to 1968 and as his country's Minister for Health and later as Minister for Education, introducing a revolutionary Free Secondary and Third Level education system in Ireland, which is credited with the subsequent large upsurge in the Irish economy. On Donogh O'Malley's sudden death, aged 47, O'Malley became one of just a select few Irishmen who have been given a full Irish state funeral – others have included Michael Collins. O'Malley's funeral was attended by the then President of Ireland, Eamon de Valera who presided at the graveside.

In the mid-1990s, O'Malley was cast as Debra Winger's husband in the ill-fated feature Divine Rapture, which also starred Marlon Brando, John Hurt and Johnny Depp. The production spectacularly collapsed a few weeks into filming when Orion, the major Los Angeles production company backing the film, suddenly went bankrupt. O'Malley lived in Los Angeles for many years and after the collapse of Divine rapture he remained close to Brando. O'Malley and Brando were working on a film version of The Merchant of Venice with Brando due to play Shylock when Brando died. On Brando's death the project was subsequently picked up with Al Pacino as Shylock but O'Malley bowed out and was not involved.

O'Malley married Gabrielle (née Leavy) in 1993.

In Los Angeles, O'Malley won a Drama-Logue Best Actor Award for his 1998 performance as "Sweeney" in Patrick Marber's Dealers Choice at The Mark Taper Forum.

O'Malley has seemingly been approached many times over the years by the Fianna Fáil party to put his name forward for election in his father's constituency, then Limerick East now Limerick City, but on each occasion O'Malley declined the invitation. On the Sam Smyth Radio Show in Ireland in 2004, O'Malley stated, "The stress of politics, one of the great performance arts, killed my father at 47 – while I would like nothing better than appearing in the great theatre that is Dail Eireann [the Irish Parliament] even for just one day, I feel the price one would pay is far too high. Politics I have discovered is a thankless Business which ultimately ends in failure – no matter how well intentioned one is".

O'Malley was founder of The Sharpe's Children Foundation, a charity designed to fight poverty with education and take orphaned and destitute children off the streets of the third world and into residential primary education. The SCF was launched at Apsley House - home of the Duke of Wellington - in October 2010. Team India - sponsored by The Sharpe's Children Foundation and made up of children who lived in railway carriages at Delhi Railway Station and who played football in the railway yards - won The Street Children's World Cup in Durban, South Africa in 2010. The Sharpe's Children Foundation was chosen as World Charity of The Year in 2012 by Intellectual Property Magazine at a ceremony in The Connaught Hotel, London and was integrated with The Consortium for Street Children later that year.

In 2011, a production of Dancing at Lughnasa in which O'Malley appeared as Father Jack was nominated for an MTA AWard.

O'Malley studied at the London Academy of Music and Dramatic Art, where he appeared as Creon in Antigone with US Actress Amy Irving in his final year production. On leaving LAMDA O'Malley was a founding member of Common Stock Theatre Company, one of London's first community theatre groups, which was based in an old church on Pentonville Road in London – where Grimaldi The Clown is buried - and which took theatre to the poor of London's East End. A fellow founder member of Common Stock with O'Malley was Dame Harriet Walter

In late 2014, O'Malley appeared as Big Daddy in "Cat on a Hot Tin Roof" at Manchester's Royal Exchange Theatre. O'Malley was nominated as Best Actor at The MTA Theatre Awards - MTA stated "Cat on a Hot Tin Roof seethes with unhappy people circling the central character, patriarch Big Daddy. Daragh O’Malley blisters his way through this famous role like a raging bull with great physical presence tempered by emotional vulnerability". The Times called O'Malley's performance as Big Daddy " towering in every sense of the word "

In 2015, O'Malley was nominated for an MTA Award and STAGE Best Actor Award for his performance as Big Daddy in Tennessee Williams Cat on a Hot Tin Roof at the Royal Exchange, Manchester.

In 2017 O'Malley was nominated for a West End Offie Award for his performance as the crooked police chief Ivan in the UK Premiere of Maxine Gorky's The Last Ones at The Jermyn Street Theatre