Born in Germany, Gregor Horsch studied at the Freiburg University of Music with Christoph Henkel and later at the Royal Northern College of Music in Manchester with Ralph Kirshbaum. After graduating from the latter institution with honours in 1989, Horsch moved to the Netherlands, serving successively as principal cellist with the Netherlands Balletorkest and the Residentie Orchestra. He was appointed principal cellist of the Royal Concertgebouw Orchestra in 1997.
As the winner of the 1988 Pierre Fournier Award in London, Horsch gave numerous recitals throughout the UK and made various radio recordings for the BBC. He made his debut at the Wigmore Hall and performed at the first International Cello Festival in Manchester and during the Schubert–Britten Festival at the Queen Elizabeth Hall. Horsch was also a prizewinner at the 1989 Scheveningen International Music Competition and at the 1990 Gaspar Cassadó cello competition in Florence.
Since 2010 Gregor Horsch plays a cello built by Giovanni Battista Rogeri, formerly played and owned by principal cellist Jean Decroos. This cello was purchased purchased by RCO Foundation together with a number of individuals and given on loan to Gregor Horsch.