"He will undergo home-based high care at his Houghton home until he recovers fully," the organization said on its website, nelsonmandela.org.
Mandela, 94, president from 1994-1999, retired from public life in 2004 and was last seen in public in 2010, when he attended the closing ceremonies of the World Cup in Johannesburg.
South African President Jacob Zuma said after visiting Mandela Christmas morning the former president was "in good spirits," Britain's The Guardian newspaper reported.
"He was happy to have visitors on this special day and is looking much better," Zuma said. "The doctors are happy with the progress that he is making."
Mandela is being treated for gallstones and a lung infection.