Kohli, who will lead India in the World Test Championship final against New Zealand at the Hampshire Bowl in Southampton from Friday, has 814 points.
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Keeping Kohli company in the top 10 is flamboyant Indian wicketkeeper batsman Rishabh Pant (747 points) and star opener Rohit Sharma (747 points), who have retained their joint sixth position.
Smith, who claimed the top spot for the first time since the Boxing Day Tests last year, takes over from New Zealand captain Kane Williamson, who is set to lead his team in the WTC final.
Williamson, who missed the second Test against England due to injury, has slipped five points behind Smith’s 891 rating points and is second in the batters’ list.
This means that Smith has been at the top for 167 Tests played worldwide in total, only behind Garry Sobers (189 matches) and Viv Richards (179 matches).
In the Test bowling rankings, senior India spinner Ravichandran Ashwin continued to occupy the second place (850 points), behind Australian fast bowler Pat Cummins (908 points).
Ashwin is the lone Indian in the top 10.
West Indies’ Jason Holder retained his top position in the Test all-rounder rankings with 412 rating points. India’s Ravindra Jadeja (386 points) and Ashwin (353) are second and fourth respectively.
Kiwi pacer Matt Henry’s player of the match performance has lifted him to a career-best 307 points and 64th position while Ajaz Patel too is at a career-high points tally of 323. Devon Conway continues his good run and is in joint-61st position.
The rankings update also includes performances from the first Test between South Africa and the West Indies in St Lucia. Quinton de Kock finds himself in joint-12th position with Cheteshwar Pujara while his compatriot Adrian Markram has advanced two slots to reach 14th position.
De Kock has gained 11 positions to attain his highest position since December 2019.
Formerly top-ranked Kagiso Rabada has gained two spots to reach seventh place after a five-wicket haul in the second innings, Anrich Nortje is up into the top 30 for the first time in his career, while Lungi Ngidi is up 14 places to 44th position with a first-innings five-wicket haul.