Oliver's riding career started in 1988 and he completed his apprenticeship with Lindsey Rudland and Lee Freedman. His first win as an apprentice was in March 1988 on Mr. Gudbud, at Bunbury, Western Australia and his first feature race win was the AJC Warwick Stakes. Unfortunately he suffered a series of injuries including a broken spine in 1996, sustained in a fall at Moonee Valley. He returned to riding after that back injury and rode the Japanese horse Pop Rock in the 2006 Melbourne Cup, which finished second to stablemate Delta Blues. In the 2007 Melbourne Cup, he placed second to Efficient on English horse Purple Moon.
Oliver has won the Melbourne Cup three times, on Doriemus (1995) Media Puzzle (2002) and Fiorente (2013), the Caulfield Cup on Mannerism (1992), Paris Lane (1994), Doriemus (1995), and Sky Heights (1999), the Cox Plate on Dane Ripper (1997) and Northerly (2001) and the Blue Diamond Stakes (2004). He was also the regular rider of Lee Freedman's champion sprinter Schillaci (1991–95) and top filly Alinghi (2003–05). In the 2007 Golden Slipper, Damien completed the grand slam of Australian racing by winning the two-year-old race on the John Hawkes trained Forensics.
On 22 September 2010, Oliver pulled out of rides at a Sandown meeting, while helping police with their inquiries into a criminal investigation.
In 2011, The Cup, a biopic starring Stephen Curry, was released. It covered Oliver's relationships with his family and the 2002 Melbourne Cup win on Media Puzzle.
In 2013, Oliver won his third Melbourne Cup riding the favourite, Fiorente. This ride was also his 100th Group 1 win. The victory was trainer Gai Waterhouse's first victory in the Melbourne Cup.
As of 17 August 2014, Oliver has ridden in 7070 races and been placed in 2970 races including 1199 wins. Total prize money for horses ridden by Oliver is over $118 million.
As of 27 July 2015, Oliver has ridden 760 rides in 2015 for 116 wins - averaging a winner every 6.6 rides.
In 2012, Oliver was accused of placing a $10,000 bet on a rival horse, Miss Octopussy, to beat a horse he was riding, Europa Point, in the same race at Moonee Valley Racecourse on 1 October 2010. Europa Point finished sixth but stewards had no issue with the way Oliver rode his horse, saying there was no change from the usual racing pattern or any other reason to doubt the integrity of the ride. It was subsequently revealed that he made an $11,000 profit with his bet. The then alleged incident was not discovered until 2012, during an investigation into the racing industry. He was subsequently dropped from the Lloyd Williams-owned Green Moon in the 2012 Cox Plate and 2012 Melbourne Cup although he did ride in the 2012 Cup Carnival, a move that reportedly annoyed some members of the public and racing industry. He won the Victoria Derby and Emirates Stakes.
On 13 November 2012, Oliver was formally charged with the alleged offence. On 20 November 2012 he was banned for eight months for the illegal bet and received an additional two months' suspension for using a mobile phone in the area of the jockeys room against the rules. He was unable to ride in races until 13 September 2013.
On his return to race riding, Oliver immediately tasted success culminating in his Melbourne Cup winning ride. There has been discussion on whether Oliver's sentence was adequate and the sentence for this offence has increased significantly since. Had it occurred in 2013, he would have been suspended for two years for the same offence.
Damien Oliver has won Racing Victoria's Scobie Breasley Medal seven times (1996, 1999, 2001, 2002, 2003, 2004 and 2014). The award recognises excellence in race riding on Melbourne racetracks.
In 2014, He won the inaugural Roy Higgins Medal as the winner of the Victorian jockeys’ premiership.
Oliver won the 2014/15 Melbourne Jockey's Premiership after riding 60 race winners. It was Oliver's 10th win of the award, trailing only Roy Higgins and Bill Duncan who have won the award 11 times.
Oliver is married to Trish and they have three children. They live in the Melbourne suburb of Port Melbourne.
Oliver's elder brother Jason was also a jockey; he died on 29 October 2002, after a fall at Belmont Park Racecourse, Western Australia when a young horse he was riding broke both front legs and fell during a race trial. The horse was found to have been administered phenylbutazone prior to the trial and this was thought to be a contributing factor in the accident.
Oliver supports the West Coast Eagles in the Australian Football League.