Greeff represented the Eastern Province Country Districts side at the 2007 Under-18 Academy Week competition before moving to Cape Town to join Western Province. He played for the Western Province U19 side in 2008 and for the Western Province U21 side in 2009 and 2010.
In 2011, he also made a single appearance for the Maties in the Varsity Cup.
He made his senior debut for Western Province in the 2010 Vodacom Cup competition, coming on as a late substitute in their match against the Boland Cavaliers.[1] He made another three appearances in that competition, as well as one in the 2011 Vodacom Cup and another in a compulsory friendly match against Boland Cavaliers prior to the 2011 Currie Cup Premier Division.[2]
He joined Johannesburg-based side the Golden Lions in 2012, where he was immediately included in their Super Rugby side, the Lions. He made his Super Rugby debut in the second match of the Lions' 2012 Super Rugby season, starting their match against the Hurricanes.[3] He made one more start (against the Bulls),[4] as well as three substitute appearances. He also made one appearance for the Golden Lions in the 2012 Vodacom Cup, but then suffered a leg fracture,[5] which ruled him out of the remainder of the season.
He returned the following season, making one appearance in the 2013 Vodacom Cup and two in the 2013 Currie Cup Premier Division, but fell out of favour and joined the Leopards for a loan spell during the 2013 Currie Cup First Division and Griquas in 2014.[6]
He joined Nelspruit-based side the Pumas for the 2016 season.[7]