Bumrah becomes first Indian pacer to top test rankings after Visakhapatnam heroics
He claimed nine wickets in his reverse swing masterclass to secure India's series-levelling victory by 106 runs.
It helped him leapfrog Australia's Pat Cummins, South African Kagiso Rabada and team-mate Ravichandran Ashwin in the official rankings, the International Cricket Council (ICC) said in a statement on Wednesday.
India spinners Ashwin, Ravindra Jadeja and Bishan Singh Bedi had earlier topped the test rankings for bowlers.
Bumrah was adjudged player of the match in Visakhapatnam ahead of team-mate Yashasvi Jaiswal, who smashed his maiden test double hundred in that match.
Left-handed opener Jaiswal moved up 37 places to 29th in the test batting rankings led by New Zealand stalwart Kane Williamson.
India's third test against England scheduled in Rajkot begins on February 15.