It will mark the trio’s first TV show since they exited Top Gear after Jeremy Clarkson punched a producer.
May joked on Twitter that the location was “chosen by Richard Hammond, who’s run out of biltong”.
When one South African fan asked if the news was true, Hammond confirmed and suggested the team hold a braai – Afrikaans for barbecue.
“Yes, for real. We’ll have to have a Bra, a Bray, a, oh you know, a South African barbecue,” he wrote.
The show will launch on Amazon Prime in the autumn, with each episode’s pre-recorded studio items filmed in a different country.
Photos uploaded to The Grand Tour’s Facebook page show the trio have already begun shooting in Portugal, Germany, Barbados and North Africa.
Jay Marine, vice president of Amazon Video Europe, said: “Given the popularity of Jeremy, Richard and James in South Africa, Johannesburg is a fantastic place to start.”
Last year, Clarkson was suspended from Top Gear and later fired by the BBC after he punched Top Gear producer Oisin Tymon.
Hammond and May quit the show shortly after.
The trio were replaced on the show by former Friends actor Matt LeBlanc, BBC Radio 2 DJ Chris Evans, and an extensive cast of co-presenters.
The new series of Top Gear made its debut on Sunday to more than four million viewers and mixed reviews.