Graaff is replacing Ismail Ould Cheikh Ahmed at UNMEER, after the Mauritanian diplomat was appointed to special UN envoy for Yemen.
Graaff will work closely with Special Envoy on Ebola David Nabarro, along with governments in the region.
UN Secretary-General Ban Ki-moon "expresses his sincere gratitude to Mr Ould Cheikh Ahmed for his exceptional work and leadership of UNMEER, and for his commitment to ensuring the affected countries are on the road to recovery from the unprecedented Ebola outbreak," a statement read.
The World Health Organization says more than 26,000 people have been infected with Ebola since the outbreak began late 2013, and more than 10,800 have died.
More than 99 per cent of the cases were reported in Liberia, Guinea and Sierra Leone.
Graaff previously worked for the WHO in several African countries, Afghanistan and Haiti, and led the Civil Affairs and Development team for the United Nations Assistance Mission in Afghanistan, or UNAMA.