Kohli, who achieved the feat in his 205th innings, surpassed India legend Sachin Tendulkar, who did it in 259 innings in 2001.
He got to 10,000 runs with a single off spinner Ashley Nurse in his 213th ODI.
The 29-year-old is the 13th batsman to reach the milestone and the fifth Indian.
Kohli made his ODI debut against Sri Lanka in August 2008.
The historic run against West Indies was part of his 37th ton in ODIs as he made an unbeaten 157 from 129 balls in India's total of 321-6 from 50 overs. The match ended in a tie as Shai Hope, who finished unbeaten on 123, scored a four off the final ball.
Kohli still has some way to go to break Tendulkar's all-time ODI run record however, with the former India skipper having made 18,426 runs before his retirement from the format in 2012.
Sri Lankan Kumar Sangakkara is second on 14,234 with Australia's Ricky Ponting on 13,704.