Bumrah has been named in the 17-member team for the series, which starts from January 5 in Cape Town.
Wicketkeeper-batsman Parthiv Patel has also found a spot in the Test squad.
All-rounder Hardik Pandya, who had been rested for the Sri Lanka Tests, has also made a comeback in the squad.
India team: Virat Kohli (capt), M Vijay, KL Rahul, Shikhar Dhawan, Cheteshwar Pujara, Ajinkya Rahane (vice-capt), Rohit Sharma, Wriddhiman Saha (wk), R Ashwin, Ravindra Jadeja, Parthiv Patel, Hardik Pandya, Bhuvneshwar Kumar, Mohammed Shami, Ishant Sharma, Umesh Yadav, Jasprit Bumrah.
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