Roy Hodgson's men earned their elevation courtesy of last Wednesday's 2-1 win over Brazil at Wembley.
World and European champions Spain remain top of the rankings with Germany and Argentina second and third respectively.
The Republic of Ireland are also up two places to 39th, while Scotland rose five places to 64th following the 1-0 win over Estonia in Gordon Strachan's first game as manager.
Wales' win over Austria moved them up 13 places to 68th but Northern Ireland dropped out of the top 100 following their draw with Malta.
The African Cup of Nations had a significant bearing on the new rankings with winners Nigeria rising 22 places to 30th, runners-up Burkina Faso moving from 82nd to 55th and Ivory Coast at a best-ever 12th.