Vettori was appointed captain of the Black Caps after former skipper Stephen Fleming stepped down as one-day captain following the World Cup in the West Indies earlier this year.
Fleming said he wanted to continue to lead the Test side but the selectors opted for a complete change, putting Vettori, 28, in charge for all matches.
The tall left-arm spinner had his first taste of leadership when he skippered the Black Caps to the semi-finals of the recent World Twenty20 in South Africa but taking on the host country in two Tests and three one-day internationals is likely to be an altogether more challenging task.
New Zealand were beaten 2-0 in a three-Test series in South Africa two seasons ago after losing a one-day series 4-0.
One of the key players for Vettori in the Test matches will be his predecessor, Fleming, who has been picked as a specialist batsman. On the 2005/06 tour Fleming made 262 in the drawn second Test in Cape Town, a record score by any visiting batsman in a Test in South Africa.
But Vettori has high hopes for his pace attack, spearheaded by Shane Bond, Mark Gillespie and Chris Martin, on pitches in Johannesburg and Centurion which usually favour fast bowlers.
On the previous tour Fleming identified South Africa's fast bowlers, Makhaya Ntini and Dale Steyn, as the difference between the two teams. Bond had to withdraw from the series because of injury, while Gillespie had not yet broken through.
Unusually for modern tours, New Zealand have a lengthy build-up to the Test matches. They arrived in South Africa last Friday and have had almost a week to prepare for Thursday's match against a capable Invitation team, led by recent Test batsman Boeta Dippenaar.
They have another four-day game, against South Africa A, before the first Test starts in Johannesburg on Nov 8.
New Zealand squad: Daniel Vettori (captain), Craig Cumming, Michael Papps, Stephen Fleming, Scott Styris, Ross Taylor, Jacob Oram, Brendon McCullum, Shane Bond, Mark Gillespie, Jeetan Patel, Michael Mason, Chris Martin, Iain O'Brien.
SA Invitation XI: Boeta Dippenaar (captain), Morne van Wyk, Imraan Khan, Ahmed Amla, Davy Jacobs, Zander de Bruyn, Thami Tsolekile, Thandi Tshabalala, Monde Zondeki, Lonwabo Tsotsobe, Yusuf Abdullah.