Stephen McGown was freed on Saturday and is now back in South Africa, Clayson Monyela said.
His father, Malcolm McGown, told a news conference in Pretoria that he was grateful to the South African government and everyone else involved in gaining his son's release.
"It took a long time but we got there -- and I'm pleased to say that my son is looking well and very healthy and his mind seems as sharp as ever," he said.
Speaking at the same news conference, South African Minister for International Relations Maite Nkoana-Mashabane voiced her condolences for the death of McGown's mother, who died in May while he was still in captivity.
Nkoana-Mashabane said no ransom was paid for McGown's release and that it had been secured with the help of "cooperation and collaboration" from the family.
His father said it had been a "big surprise" when Stephen came back, "but when I gave him a hug he felt as sound and as strong as before, so he was well treated up there.
"Obviously the joy of the miracle that happened ... we can't describe it. I guess unless you have actually traveled the road, you really don't know what it's like."
Malcolm McGown said he regretted that his wife had not lived to see their son again, but he believed Stephen would "pick himself up in a little while's time and join the normal run of life."
Stephen McGown did not appear at the news conference himself, although his wife Catherine and mother-in-law were present alongside his father.
"It's been a very, very long time and I'm pleased, just so pleased, that this day has come," his wife said. "It's just unfortunate that Steve's mum isn't here and that Steve isn't here right now."
The moment when she and her husband were finally reunited was like none of the scenarios she had imagined over the years, she said.
"The first thing he said to me was, 'Your hair has grown.' I said to him 'Actually, your hair is longer than mine now,'" Catherine recalled.
Doctors are still attending to McGown and will continue to monitor his health, Monyela said earlier.
McGown was taken hostage while on vacation in Timbuktu, northern Mali, along with Swedish national Johan Gustafsson and Dutch national Sjaak Rijke.
Gustafsson returned to Sweden
in June this year after being released by his captors, Swedish authorities said.
Rijke was freed in April 2015 by French special forces, the French Defense Ministry said at the time.
Dr. Imtiaz Sooliman, chairman and founder of African NGO Gift of the Givers, said the charity had started negotiations for McGown in June 2015 after his father asked for help but was not involved in the final stages of McGown's release.
The South African government worked alongside the charity from 2015, Sooliman said. Gift of the Givers also negotiated for the release of Gustafsson, he added.