During the third and final T20I in Pune, Kohli became the second Indian after MS Dhoni and sixth overall in the history of cricket to amass 11,000 runs as captain in the international circuit.
In the second T20I, Kohli also went past 1,000 runs as captain in the shortest format. India, after beating Sri Lanka 2-0 in the three-match Twenty20 International series, are set to host Australia for three One-Day Internationals, starting January 14.
The first ODI will be played in Mumbai on Tuesday while Rajkot and Bengaluru will host the last two games respectively.
After the home series against Australia, India will travel to New Zealand where they are scheduled to play a full tour, including five T20Is, three ODIs and two Tests.
The two Test matches will be a part of the World Test Championship, where India sit on top of the points table with 360 points from seven wins out of seven games.