Hauser was born in Pula, Croatia, into a musical family, where he began his musical education. His mother plays percussion. His sister is a journalist in Pula.
Hauser finished secondary school in Rijeka. He studied in Zagreb but completed his undergraduate studies with Natalia Pavlutskaya at Trinity College of Music (now Trinity Laban) London. He completed his postgraduate studies with Ralph Kirshbaum as a Dorothy Stone Scholar at RNCM in Manchester and with Bernard Greenhouse in USA.
Hauser has performed in more than 40 countries including successful debuts in Wigmore Hall, Royal Albert Hall, Amsterdam Concertgebouw, Southbank Centre and many more.
In October 2006 Hauser was the only cellist chosen to perform at the gala at Palazzo Vecchio in Florence for the late Mstislav Rostropovich. Following the success of this appearance, Stjepan has been invited to perform at the most prestigious festivals in Europe. At the International Holland Music Sessions 2009, he was chosen to participate in the “New Masters on Tour” concert series, presenting young artists in prestigious concert venues all over the continent.
In December of 2007, Hauser played the Kol Nidre with the Metropolitan Sinfonia at a Gala Tribute Concert dedicated to Mstislav Rostropovich.
Subsequently, Hauser went on to perform and record as a solo artist including his recording of British composer Christopher Ball’s First Concerto for Cello, written by the composer specifically for him. The album, Christopher Ball: Music for Cello, was recorded at the first live performance of the concerto in 2010, and features former Greenwich Trio member, Yoko Misumi, on piano.
On 11 June 2009 Hauser launched his channel on YouTube, which has since reached over 270 million views as of May 2020. In January 2011, Hauser, along with friend and fellow cellist Luka Šulić, performed a cover of Michael Jackson’s “Smooth Criminal” which was played solely on cello. In just a few days, the music video for this cover became a YouTube sensation.
The album Hauser Classic was released on 7 February 2020, in which he plays alongside the London Symphony Orchestra. The album was produced by multi award-winning record producer Nick Patrick.
During the COVID-19 quarantine, unable to tour in support of his solo album, Hauser released three performances via live streaming. The first, Hauser: Alone Together, released on 27 April 2020 was performed at the Arena Pula, in Stjepan’s hometown of Pula, Croatia on the Istrian peninsula. The second, also titled Hauser: Alone Together, was performed at Krka National Park, at the Krka Waterfalls in central Croatia. The second video was released on 15 June 2020, to celebrate the artist’s 34th birthday. The third, again titled Hauser: Alone Together, was recorded at Fort Lovrijenac in Dubrovnik, Croatia, recognisable to many fans from the HBO series, Game Of Thrones. A special 2 disc edition of Hauser Classic is scheduled for October 2020 release. It includes a DVD of the three Hauser: Alone Together videos.
The album Hauser plays Morricone is set to premiere on YouTube on October 27, 2020 .
Hauser performs many of his pieces barefoot.