Greg first started to get noticed as a world class downhill racer at the age of 17, in 1999, racing select World Cups (including one in his home country of South Africa, in Stellenbosch) on a local shop team, aboard a Kona Stab Dee-Lux bike with a Marzocchi Monster T. fork. In 2000, he was picked up as a junior by British international team Animal Orange, which used Orange frames (222 for downhill and Ms. Isle for dual slalom) and RockShox suspension. That year Greg podiumed at a World Cup points series race for the first time.
The following two years Greg rode for the Global Racing team, aboard similar bikes to the previous years', and on this team, at the age of 19, he won the overall World Cup points series in the Elite downhill. In 2003 Greg switched to the Haro Lee Dungarees team, which used Intense designed and built DHR frames for the dowhill and their own short travel Werx trailbike frames for Four Cross, with Manitou suspension. It was aboard this team that, at the age of 21, Greg became World Champion of downhill.
In 2004, Greg was offered a spot on Team G Cross Honda, which used one-off internally geared frames made by Honda, with a Showa suspension. He accepted and stayed for four years, winning his second World Cup points series overall victory in 2005. The 2007 season ended on a bittersweet note with a dislocated and fractured shoulder early in his winning World Championship final run although Greg got back on the bike to salvage a painful 4th-place finish. In addition, Greg was forced to switch teams yet again when Honda pulled out of the sport and he chose the Santa Cruz Syndicate team, alongside riders Steve Peat, Nathan Rennie, and Josh Bryceland for the 2008 season.
Minnaar was appointed as a member of the inaugural UCI Athletes' Commission in 2011.
Minnaar has won the UCI Downhill World Championship three times - in 2003, 2012 and 2013. He has finished second four times (2004, 2006, 2009 and 2015) and taken the bronze three times (2001, 2005 and 2010).
Minnaar has been crowned Downhill World Cup champion three times (2001, 2005 and 2008) for winning the Mountain Bike World Cup points series. He was also crowned Downhill World Champion in 2003 for winning the season ending event. He has also done well in the Four Cross event, with one win in the 2003 World Cup points series, in Fort William, Scotland, and a fourth-place finish at the 2005 World Championships.
In the 2008 World Cup, Minnaar podiumed at every one of the seven events in the series, taking the win at Fort William, Mont-Sainte-Anne and Canberra. This gave him a comfortable lead going into the finals at Schladming, Austria, where he placed fifth and clenched his overall lead to take the well-deserved title.
In the 2009 World Cup series, Minnaar took first place at Pietermaritzburg South Africa, Fort William Scotland and Bromont Canada. He also came 6th at La Bresse in France, 3rd at Vallnord in Andorra, Maribor in Slovenia and in Schladming Austria. Greg also came 22nd in Mont-Sainte-Anne leaving him with a 2nd place overall. In the World Championships at Canberra Australia he lost 1st place to his team mate Steve Peat by 0.05seconds
In the 2015 World Cup series, Minnaar took first place at Lenzerheide, Switzerland, earning him his 18th career win and setting the record for most world cup wins in the history of downhill racing. Until this victory, Minnaar had shared the record for most overall world cup race wins with Santa Cruz Syndicate teammate Steve Peat, after a victory earlier in the 2015 season
Minnaar was twice (2003, 2004) crowned champion of the NORBA (now USA Cycling) points series.2017
1st DH, UCI Mountain Bike World Cup, Fort William, Scotland
1st DH, UCI Mountain Bike World Cup, Lenzerheide, Switzerland