Kohli will captain a 15-member Indian side for the ODIs, while also leading a 15-member squad for the T20I series against visitors England.
The right-handed batting talisman was handed the captain's role following MS Dhoni's decision to step down as skipper on Wednesday.
Among the most prominent selections, Yuvraj Singh has been named in both the ODI and T20I squads.
Earlier, the BCCI selection meet was postponed by almost three hours on Friday in Mumbai due to logistical reasons generated by the Supreme Court ruling, which made most Board of Control for Cricket in India officials ineligible.
The confusion started when former joint secretary Amitabh Choudhary asked CEO Rahul Johri as to why he has not been intimated about the meeting to pick the team for the limited-overs series against England as the BCCI constitution states that only he can convene the meeting.
The Lodha committee secretary Gopal Shankarnarayan in a clearly worded e-mail informed Johri that former joint secretary Amitabh Choudhary "stands disqualified" in the wake of SC order on January 2 and 3 and can't convene the selection meeting as secretary Ajay Shirke has also been sacked by apex court.
The e-mail sent by Shankarnarayan to Johri states: "The Committee is in receipt of your email. It is clarified that Mr. Amitabh Choudhary stands disqualified and is no longer the joint secretary of the BCCI or an office bearer of the BCCI or a State Association by virtue of the orders of the Supreme Court dated 2.1.2017 and 3.1.2017.
"As a result, he has no authority to interfere with the BCCI and it's functioning or with the directions of this Committee. Please proceed with the Selection Committee Meeting as scheduled," the email further states.
After a delay of one hour from the scheduled time, BCCI CEO Rahul Johri sent an e-mail to Shankarnarayan, intimating him about an e-mail from Amitabh Choudhary and seeking directive about the scheduled selection meeting.
"I have received an email from Mr. Amitabh Choudhary, the Joint Secretary of BCCI requesting that the said meetings be postponed till evening so that he can convene and attend the same.
"We have received differing legal advice insofar as whether a person who has completed 9 years as an office bearer of a State Association would be disqualified from being an office bearer of the BCCI in terms of the order dated 2nd January 2017 read with the order dated 3rd January 2017 and have been advised to seek a clarification from the Hon'ble Supreme Court."
Johri had informed the panel secretary that Choudhary is yet to complete nine years as an office-bearer in BCCI.
"Although Mr. Amitabh Choudhary has completed 9 years as an office bearer of a State Association, he has not completed 9 years as an office bearer of BCCI."
ODI squad: KL Rahul, Shikhar Dhawan, Virat Kohli (c), MS Dhoni, Manish Pandey, Kedar Jadhav, Yuvraj Singh, Ajinkya Rahane, Hardik Pandya, Ravichandran Ashwin, Ravindra Jadeja, Amit Mishra, Jasprit Bumrah, Bhuvneshwar Kumar and Umesh Yadav.
T20I Squad: KL Rahul, Mandeep Singh, Virat Kohli, MS Dhoni, Yuvraj Singh, Suresh Raina, Rishabh Pant, Hardik Pandya, Ravichandran Ashwin, Ravindra Jadeja, Yuzvendra Chahal, Manish Pandey, Jasprit Bumrah, Bhuvneshwar Kumar and Ashish Nehra.
1st Warm-up on January 10 in Mumbai (1:30pm IST)
2nd Warm-up on January 12 in Mumbai (9:00am IST)
1st ODI on January 15 in Pune (1:30pm IST)
2nd ODI on January 19 in Cuttack (1:30pm IST)
3rd ODI on January 22 in Kolkata (1:30pm IST)
1st T20I on January 26 in Kanpur (4:30pm IST)
2nd T20I on January 29 in Nagpur (7:00pm IST)
3rd T20I on February 1 in Bengaluru (7:00pm IST)
(With PTI inputs)