His first win came at Limerick in 1987 with Chicago Style when he was an apprentice to trainer John Oxx, and was first presented with the award of Champion jockey of the year in Ireland in 1989, then again in 1996, and the third time in 1998.
In 1995, he claimed his first Irish jockeys' championship, and together with Ridgewood Pearl, took the 1995 Breeders' Cup Mile at Belmont Park. 1999 concluded with a win at the Ascot Gold Cup with Enzeli and the Irish National Stakes with Sinndar.
In 2000, jockey Kieren Fallon was injured and Murtagh's services were called upon by Sir Michael Stoute. During his time with Stoute, Murtagh accomplished a group 1 treble, winning the Prix de l'Opera on Petrushka, the Prix de l'Abbaye on Namid and the Prix de l'Arc de Triomphe on Sinndar at Longchamp, and wrapped up the year with the 2000 Breeders' Cup Turf on Kalanisi.
2001 proved to be more challenging than the previous year, and he only brought home the Irish 2000 Guineas and the St James's Palace Stakes on Black Minnaloushe respectively, and the Ascot Gold Cup with Royal Rebel.
The English 2000 Guineas on High Chaparral, and the Epsom Derby aboard Rock of Gibraltar saw Murtagh into 2002 in style, repeating his win with Royal Rebel in the Ascot Gold Cup, followed by his 2003 victory on Alamshar in the Irish Derby, the King George VI and Queen Elizabeth Diamond Stakes.
Murtagh's high point of 2005 was with Motivator in his third Epsom Derby win.