Kohli, who took over the captaincy reign from Dhoni earlier this month, achieved the feat during the third and final ODI match against England at the Eden Gardens in Kolkata.
Kohli achieved the milestone in 17 innings, beating AB de Villiers’s record. The South Africa skipper had scored 1000 runs in 18 innings.
Kohli is the seventh Indian batsman to achieve the feat.
Dhoni leads the list with 6,633 runs, followed by Mohammad Azharuddin (5,239), Sourav Ganguly (5,082), Rahul Dravid (2,658), Sachin Tendulkar (2,454) and Kapil Dev (1,564).
Fastest to 1000 runs as ODI captain (by innings)— Sarang Bhalerao (@bhaleraosarang) January 22, 2017
17 - VIRAT KOHLI
18 - AB de Villiers
20 - Kane Williamson #INDvENG
Fewest inns to 1000 runs as ODI captain— Mohandas Menon (@mohanstatsman) January 22, 2017
17 Virat Kohli
18 AB deVilliers
20 Kane Williamson
21 Alastair Cook
22 Sourav Ganguly#IndvEng
1000 runs for Virat Kohli as ODI captain.He is the fastest to do so - in just 17 innings. ABDV had reached the mark in 18 innings.#INDvENG— Rajneesh Gupta (@rgcricket) January 22, 2017