The 32-year-old has overcome a succession of injuries and returned to domestic action, proving his fitness for the series in India.
His presence will in part make up for the injury absence of fast bowler Kagiso Rabada, who has been ruled out for four weeks with a rib problem.
"We know exactly what he (Nortje) brings so we’re really looking forward to working with him," South Africa coach Shukri Conrad said.
"Of course we'll miss KG (Rabada) on this tour, but as we saw in the first test win over India, this group has depth and that is one of our primary goals as a squad, to develop a unit filled with players who can step up at any time."
South Africa also named a squad for the three-match one-day international series that will be played ahead of the T20s.
It contains many of the same players who did duty on the recent tour of Pakistan, with experienced wicketkeeper-batter Quinton de Kock selected for both the ODI and T20 squads.
The ODI series will be played from November 30 to December 6, with the five T20s from December 9-19.
The teams complete their test series with a second and final fixture that starts on Saturday.
South Africa ODI squad:
Temba Bavuma (captain), Ottneil Baartman, Corbin Bosch, Matthew Breetzke, Dewald Brevis, Nandre Burger, Quinton de Kock, Tony de Zorzi, Rubin Hermann, Keshav Maharaj, Marco Jansen, Aiden Markram, Lungi Ngidi, Ryan Rickelton, Prenelan Subrayen.
South Africa T20 squad:
Aiden Markram (captain), Ottneil Baartman, Corbin Bosch, Dewald Brevis, Quinton de Kock, Tony de Zorzi, Donovan Ferreira, Reeza Hendricks, Marco Jansen, George Linde, Kwena Maphaka, David Miller, Lungi Ngidi, Anrich Nortje, Tristan Stubbs.