"Thank you Patrick and Basu for the amazing work you both have done for the team," Kohli said in a tweet after India were knocked out by New Zealand in the semifinal by 18 runs on Wednesday.
Kohli also termed the camaraderie both of them shared with the players as "special".
"More importantly, the friendship you have with all of us is even more special. You both are true gentlemen. Wish you the best for everything else in life ahead," he added.
India will now be in the lookout for their replacements ahead of the tour of the West Indies next month.
Australian Farhat joined the team in 2015 with almost three decades of professional experience behind him. Basu helped the players with their physical fitness and also with their diet.
Previously, Basu was with the Indian Premier League (IPL) franchise Royal Challengers Bangalore led by Kohli.