Johnson (884) leads India’s Ravichandran Ashwin by 13 points, who maintained the second position with 871 points.
Ravindra Jadeja, another Indian featuring in the top ten, maintained his sixth position with 789 points.
Anderson took three for 36 in the first innings and five for 58 in the second, leapfrogging team-mate Stuart Broad and Ashwin to the coveted number-one position.
Anderson is the fourth England bowler to top the bowlers’ table since Ian Botham first achieved this feat in 1980. Steve Harmison stormed up the chart in 2004, while Broad vaulted to the number-one position earlier this year following the Johannesburg Test against South Africa.
Broad, who took five wickets in the Test, has slipped behind Ashwin to third place after conceding three points.
Other bowlers to improve their rankings post the Chester-le-Street Test are Nuwan Pradeep (43rd, up by five places), Milinda Siriwardana (50th, up by 13 places) and Chris Woakes (73rd, up by 16 places). In the batting table, England s Moeen Ali has achieved a career-high ranking of 35.
The left-handed batsman scored 155 not out, his career-best score in 25 Tests, which helped England to declare its first innings at 498 for nine.
For this achievement, Ali has earned 82 points that has lifted him 12 places to a career-high 35th position in the Rankings for Test Batsmen.
Opener Alex Hales has also continued to head in the right direction. After scoring 83 and 11, the 27-year-old batsman has moved up nine places to 70th. In the past two Tests, Hales has claimed 47 places and looks strong to gain further spots as he is still in the qualification period.
A batsman qualifies for a full rating after he has played 40 Test innings, while Hales has so far batted in only 11 Test innings.
Sri Lanka s Dinesh Chandimal, who scored 126 in the second innings, has moved up one place to 19th, while Nick Compton is now in 67th spot after rising one place.
Alastair Cook, who became the first England batsman to complete 10,000 Test runs while scoring 47 not out in the second innings, has retained his 15th position.
Australia captain Steve Smith is the number-one ranked Test batsman, followed by Joe Root of England and New Zealand s Kane Williamson.
In the all-rounders list, Ali has gained one place and is now sixth, just one point behind team-mate Ben Stokes. Ashwin ranked number one all-rounder.