Cameroon were stripped of hosting rights in November over preparation delays and security concerns.
Cameroon has faced persistent attacks by Boko Haram militant in the north and a conflict between the army and separatists in the two English-speaking regions in the west.
South Africa has much of the necessary infrastructure after hosting the 2010 World Cup and the 2013 Africa Cup of nations.
The 2006 hosts Egypt would also appear to have the infrastructure but only expressed its interest in hosting the tournament on December 14 after Morocco pulled out in the middle of the same month.
This year's competition will run from June 15 to July 13.