Ravichandran Ashwin (85* off 207) was nearing his third Test hundred while batting alongside Wriddhiman Saha (22* off 62) when drinks were called in the second session.
Kohli, who reached his maiden double hundred in Tests just before lunch, played second ball after the break on to his stumps.
The Indian captain had cantered to his double century as India cruised to 404 for 4 at lunch.
Kohli (200 off 283 balls ), resuming at an overnight 143, reached the milestone at the stroke of lunch and was ably supported by Ashwin.
The double century was also first for Kohli at the First Class level with his previous highest being 197.
India had started off the day at their overnight score of 302/4, with the two batsmen looking to bat as long as possible. And it was obvious from their watchful demeanour, as the West Indies had opted for the new ball straightaway. Shannon Gabriel and Jason Holder then started off the proceedings, as on day one, but the pitch seemed to have eased out considerably as compared to the first morning.
Meanwhile, Kohli continued his march without any discomfort at all. First up, he crossed the 150-mark off 208 balls as the 100-partnership came up in the 96th over. Then he went past his previous Test highest score of 169 scored against Australia at the MCG in December 2014.
Ashwin made good of the life given to him and reached his seventh Test fifty off 127 balls. In doing so, he helped India past the 400-mark in the 118th over and indeed brought up the 150-partnership with Kohli off 272 balls. The West Indies were looking lethargic in the field as the partnership sucked out all energy, even as the wait was now for Kohli's impending milestone.
He beat Mohammad Azharduddin's long-standing record of 192 against New Zealand scored in February 1990.
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