Test captain Kohli, 28, takes charge for the three one-day internationals, starting on 15 January, and three subsequent Twenty20 internationals.
MS Dhoni, who stepped down as skipper on Wednesday, is in both squads, as is recalled all-rounder Yuvraj Singh.
However, uncapped 19-year-old Rishabh Pant joins fellow wicketkeeper-batsman Dhoni in the Twenty20 squad.
After two warm-up games in Mumbai on 10 and 12 January, England face India at Pune in the first ODI on Sunday 15 January, before the series moves to Cuttack (19 January) and Kolkata (22 January).
The T20 matches take place in Kanpur (26 January), Nagpur (29 January) and Bangalore (1 February).
India ODI squad: Virat Kohli (capt), Ravichandran Ashwin, Jasprit Bumrah, Shikhar Dhawan, MS Dhoni (wk), Ravindra Jadeja, Kedar Jadhav, Bhuvneshwar Kumar, Amit Mishra, Manish Pandey, Hardik Pandya, Ajinkya Rahane, KL Rahul, Yuvraj Singh, Umesh Yadav.
T20 squad: Virat Kohli (capt), Ravichandran Ashwin, Jasprit Bumrah, Yuzvendra Chahal, MS Dhoni (wk), Ravindra Jadeja, Bhuvneshwar Kumar, Ashish Nehra, Manish Pandey, Hardik Pandya, Rishabh Pant (wk), KL Rahul, Suresh Raina, Mandeep Singh, Yuvraj Singh.
Virat Kohli has been named as India limited-overs captain for their upcoming series against England.