Mandela, 88, and his wife, Graca Machel, greeted Blair and his wife, Cherie, at his Johannesburg foundation, The Times of London reported.
"I look forward to welcoming a young man to the club of retired presidents," Mandela said. "I need to warn you, however, that some of us only become active after standing down. I know that your energy, passion and youth, mean you can still play a big role in international affairs and we look forward to the contribution you can make."
In a speech in Midrand, near Pretoria, Blair said Britain and other developed countries must support the good governments in Africa, while Africans must eliminate bad ones.
"Wealthy nations and Africa, both of us face a choice -- us, as to how far we help Africa to take the right path. Africa, as to which path to take," he said.