Off-spinner Patel and all-rounder Jimmy Neesham were the two players recalled to the squad on Friday, coming in at the expense of quick Matt Henry and batsman Dean Brownlie.
Selectors also confirmed that short-ball specialist Neil Wagner was fit for the series after a hand injury last month put him under an injury cloud.
As expected, there was no room for opening batsman Martin Guptill, despite his unbeaten 180 this week in the fourth ODI against the Proteas in Hamilton.
Match-winner Guptill fails to earn Test recall
Patel, 36, has had a stop-start 21-Test career, making his debut in 2006 but dropping off the radar from 2013-2016 before joining the Black Caps' tour of India.
After returning home, he was discarded again for Test series against Pakistan and Bangladesh but has enjoyed a strong domestic season with Wellington.
Chief selector Gavin Larsen said Patel had the ability to turn the ball away from South Africa's left-handers, complementing fellow spinner Mitchell Santner.
South Africa recall Morne Morkel for New Zealand Tests
“He brings a huge amount of experience to the team and gives us the balance of having two front-line spin options,” said Larsen.
The first Test begins in Dunedin on Wednesday followed by two more in Wellington and Hamilton later this month.
Before then, the Black Caps and South Africa face-off in an Auckland decider on Saturday for the one-day series, which is currently locked at 2-2.
New Zealand
Kane Williamson (c) Trent Boult, Colin de Grandhomme, Tom Latham, Jimmy Neesham, Henry Nicholls, Jeetan Patel, Jeet Raval, Mitchell Santner, Tim Southee, Ross Taylor, Neil Wagner, BJ Watling.
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