Anderson has so far picked up 18 wickets in the three-match series, including a 10-wicket haul in the opening test at Leeds, as he guided England to an unassailable 2-0 lead over the tourists at Chester-le-Street.
The 33-year-old became the fourth England bowler to top the test bowling rankings after Ian Botham, Steve Harmison and Broad, cricket's governing body said on its website.
Despite picking up 10 wickets in the Sri Lanka series, Broad dropped down to third, one place below Indian spinner Ravichandran Ashwin, who retained second.
Trent Boult is the highest ranked New Zealander at 7th.
Australia's Steve Smith tops the test batsman rankings, while Joe Root maintained his second place after scoring a half-century in England's second test win against Sri Lanka, while Kiwi Kane Williamson came in third.
Australia and India are first and second respectively in the test team rankings. England are fourth, while New Zealand are fifth.
