While Kohli will play in the third Test in New Delhi starting December 2, his limited overs deputy Rohit Sharma will be leading the squad in the three-match ODI series starting December 10.
Ashwin and Jadeja's continued exclusion is a clear indication that they are not in the immediate scheme of things in this format.
Shreyas Iyer, who made his T20 international debut against New Zealand last month, has earned his maiden call-up in the ODI side and is expected to bat in Kohli's place at number three.
Kaul has played for India A and has 175 wickets from 50 first-class games and 98 scalps from 52 List A (domestic 50- overs) games. The medium pacer has also been a part of IPL franchises Delhi Daredevils and Kolkata Knight Riders.
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The squad for the T20 Internationals against the islanders and the Test tour of South Africa has been put off till the third and final match in the national capital.
On expected lines, Axar Patel, Yuzvendra Chahal also came back in the squad.
It was learnt that since Kohli will be playing the third Test in Delhi, he requested the selectors to pick the squad for the South Africa Tests during that game. Chief selector MSK Prasad and his panel agreed to Kohli's request.
Off-spinner Ashwin and left-arm spinner Jadeja have now been dropped for the fourth consecutive limited overs series starting from the away games against Sri Lanka.
This was after Ashwin (8/120) and Jadeja (5/84) grabbed 13 of the 20 wickets on an unresponsive Nagpur track.
"I would not say it is cast in stone but it could well be that Indian cricket is finally moving towards the direction of having separate teams for red and white ball cricket," former India wicketkeeper and cricket analyst Deep Dasgupta told PTI.
It was learnt that both Ashwin and Jadeja have been intimated by the selectors about their intentions going into the 2019 World Cup.
Before being dropped from the ODIs, wickets had dried up for both the Test specialists. In his last 10 ODIs, Jadeja got only seven wickets while Ashwin had only 10 from his last 10 games. Their economy rates have been pretty decent with 4.90 for Jadeja and 4.91 for Ashwin.
The figures indicate that while the economy rates are pretty similar, Kuldeep and Chahal are now wicket-taking options for an attacking captain like Kohli.
Unless the two young spinners do terribly in South Africa and subsequently in England, the doors in limited overs format looks all but shut for Jadeja and Ashwin.
The squads:
India squad for the third Test: Virat Kohli (Captain), M Vijay, KL Rahul, Shikhar Dhawan, Cheteshwar Pujara, Ajinkya Rahane (Vice-Captain), Rohit Sharma, Wriddhiman Saha, R Ashwin, Ravindra Jadeja, Kuldeep Yadav, Mohammed Shami, Umesh Yadav, Ishant Sharma, Vijay Shankar