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Published 10:03 14 Jul 2016 BST
Updated 10:08 14 Jul 2016 BST
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The gain for Martin O'Neill's men is primarily down to the Euro 2016 group stage win over Italy (ranked 10), which ensured a place in the knock-out stages.
The main climbers are France, Wales and Iceland, who all excelled at this summer's championships. England and Spain are two of the sides to drop down.
As for England, Daniel Sturridge's stoppage time winner against Wales feels like a lifetime ago.
Given the way Euro 2016 panned out for England and Wales, many had suspected this was on the cards.
England, despite winning every single one of their qualifiers, never really clicked into gear in France, eventually sent packing by Iceland in the last 16. In contrast, Wales (the only side that England managed to beat) reached the last four in the tournament - their first in over half a century.
As a result, Chris Coleman's side have jumped 15 places to 11th in the FIFA rankings, leapfrogging 13th-placed England in the process.
https://twitter.com/richard_conway/status/753502159610806272
Euro 2016 winners Portugal - despite having only won one match over 90 minutes at the tournament - have risen to sixth in the list, overtaking France (seventh) who they beat in the final.
Belgium, the side that Wales made light work of in the quarter-finals, remain the highest ranked European side - sandwiched between first-placed Argentina and Colombia in third.
Iceland's heroics in France see them climb 12 places to 22nd while the Netherlands, who failed to make it to the finals in France, have dipped to 26th - their lowest ever ranking.
Scotland, also absent at the Euros, sit in 50th while Northern Ireland drop three places to 28th. Here's how the top 20 looks:
FIFA Ranking Top 20, July 2016
1. Argentina
2. Belgium
3. Colombia
4. Germany
5. Chile
6. Portugal
7. France
8. Spain
9. Brazil
10. Italy
11. Wales
12. Uruguay
13. England
14. Mexico
15. Croatia
16. Ecuador
17. Poland
18. Switzerland
19= Hungary
19= Turkey
*Additional reporting by Simon Lloyd

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