Kohli got to the landmark in the 37th over when he guided one off Grandhomme towards the third man for a four.
Mahendra Singh Dhoni had reached the milestone last year while other Indians who have done so are Sachin Tendulkar, Rahul Dravid, Sourav Ganguly and Mohammad Azharuddin.
Overall, Kohli, who played his 202nd innings today, has become the 19th batsman to breach the 9000-run mark, making him the fastest to get there.
Earlier in the series, the Indian captain had surpassed Australian great Ricky Ponting in the list of most ODI hundreds with his 31st ton.
Kohli had a quiet series against the Australians by his standards but he is back to his best against the Black Caps.