Kohli has played 86 Tests, 248 ODIs and 82 T20Is with over 20,000 international runs.
Finch said it is incredible how players like Kohli, Steve Smith, Ricky Ponting, Sachin Tendulkar tend to rarely go through bad phases.
"Every player, regardless of who it is, has a bad series. But very very rarely do you see Kohli, (Steve) Smith, even going back (Ricky) Ponting, Sachin (Tendulkar), these guys they don't have two bad series in a row," Finch said on the 'Sony Ten Pit Stop' show.
"The pressure of playing for India is one but also leading India is another and the way he (Kohli) has done it, so consistently for a long time."
"And taking over from (MS) Dhoni, the leadership, that is huge. The expectations were high and he kept delivering and I think that that is the most impressive thing," he added.
On Kohli's batting, Finch said: "What has been so impressive for so long is just his consistency across three formats. To be the best player of all-time in ODI cricket is one thing but then to also be in Test cricket and T20 cricket as a rounded player that is remarkable."
Kohli has played 86 Tests, 248 ODIs and 82 T20Is in his illustrious career so far and made over 20,000 international runs.
Under his captaincy, Team India reigned supreme in the ICC Test rankings for a long time until earlier this year and reached the final of the 2017 Champions Trophy and the semi-final of the ODI World Cup last year in the UK.
Finch, meanwhile, also spoke on the ban imposed by the ICC on the usage of saliva as a ball-applicator amid the ongoing COVID-19 pandemic.
"I haven't spoken to anyone in England or the West Indies camp on how that's (saliva ban) going to go. But that is something that the players have to adapt to over the next couple of months (or) however long that it lasts," he said.
"Finding different ways to shine the ball, because I think naturally, just out of instinct or habit, you lick the fingers and you rub the ball."
"So I am sure there will be some inadvertent mistakes. Everyone has to be really flexible and accommodating and understand that things are going to be different to what they were four months ago," Finch added.
(Inputs from PTI)