Harun has denied ICC claims that he was responsible for the murder and rape of civilians in Darfur while he served as Sudan's minister of state for the interior.
Bashir's decree to appoint Harun as governor of south Kordofan, which lies on the disputed border between north and south Sudan, comes two months after the president had war crimes charges issued against him by the ICC.
He has said that he does recognise the ICC and has repeatedly rejected calls to handover Harun and Ali Kosheib, the leader of an armed group accused of abuses in Darfur, to the court.
The decree came on the same day that the Sudanese government said that it will invite new foreign aid organisations into Darfur, weeks after Bashir ordered 13 aid agencies out of the war-ravaged region, saying they were "complicit" with the ICC.
South Kordofan lies on the border with Darfur, where at least 300,000 people have been killed and 2.7 million left homeless by war since 2003, according to United Nations estimates.
Sudan, has rejected the UN figures, saying that 10,000 people died in the war.
The province which Harun will govern includes the town of Abyei, the future of which is one of several outstanding issues in the implementation of a fragile north-south peace deal in Sudan.
Khartoum and the Sudan's People Liberation Army/Movement (SPLA/M) have failed to resolve several differences despite signing a peace deal in 2005 to end a 21-year civil war in southern Sudan, in which about 1.5 million people died.
Abyei is scheduled to hold a referendum in 2011 on whether to keep its special administrative status in the north or join the south.