Vettori, who is also Kohli's former IPL teammate and coach, said that Kohli's ability to have good discussions with the other coaches, including him and his desperation to get better is what made Virat an "exceptional" captain.
Vettori has worked with Kohli for six seasons as player and coach at the IPL franchise Royal Challengers Bangalore.
"When I used to speak to him or any other coaches (used to) speak to him, there's always a conversation around what you think is best, where can this work," Vettori said on the latest episode of ESPNcricinfo's Talking T20 podcast.
"It wouldn't always be a numbers-driven conversation, it would be around some intuition and understanding of the game. I think, ultimately, when you sold a compelling story to Virat, he was always on board, open to listen and that made him such a good captain."
Talking about Kohli's on-field personality, Vettori said his "energy, enthusiasm and desperation to win" was "contagious."
"...you couple that with (him being) the best batsman in the world, and with a work ethic that has probably led India into the situation they are now [in]. Everyone wants to follow his gym (routine), and everything he does off the field, the way he basically prepares to play the game. That's a huge part of leadership. That's a huge part of captaincy."
"For me, I think there's such a strong correlation between thorough planning and the use of data to performance. I think it's so important because I think cricket, in general, is quite immature in terms of its exposure to this.
"So, while we're in these infant stages, I think it's hard for people to get their heads around (analytics). But, the people who are gonna buy into this first, get their heads around it, I think they'll get the jump-start on everyone."