Run-machine Kohli capped a memorable 2018 by becoming the first to win the International Cricket Council's (ICC) cricketer, test and one-day international (ODI) player of the year awards last month.
Considered part of the elite group also featuring Kiwi Kane Williamson, Australian Steve Smith and England's Joe Root, Kohli has surged ahead after a stupendous 2018 and is currently the top ranked test as well as one-day batsman.
"Everything about Virat's game stands out. I think he is head and shoulders above anyone else in world cricket today," Sangakkara told India Today news channel.
"And I think going forward, he will be one of the greatest ever cricketers, if not the greatest ever," said the Sri Lankan batting great.
With 39 centuries from 222 one-day matches, Kohli is second only to compatriot Sachin Tendulkar - who scored 49 from 463 - in the 50-over century makers' list.
He has also scored 25 hundreds in 77 tests.
Sangakkara is amazed by Kohli's ability to success across formats without tinkering his basis game.
"He has this incredible knack of scoring runs and has a very, very solid method that he believes in..." said the former Sri Lanka captain.
"... if you see the tempo which he bats with, it hardly changes. He does read the situation very well.
"He is a very passionate guy, you see that in his expressions on the field... it's the overall aspect of both the person and how he has sorted his batting and his attitude."
Sangakkara's former team mate Mahela Jayawardene lauded how Kohli handled the pressure of leading the team of a cricket-mad nation of 1.3 billion.
"It's not just about the ability Virat has but to understand the way to handle pressure not just on the field but also off the field and the expectations," said the former Sri Lanka captain.
"We grew up with Sachin who had to perhaps experience the same thing. And for the next generation, it's probably on Virat's shoulders..." Jayawardene said.
(This story adds dropped word "of" in lede)
(Reporting by Amlan Chakraborty in New Delhi; editing by Sudipto Ganguly)
