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Spurs went into final round of matches occupying seventh place in the Premier League and two late goals from Gareth Bale at the King Power Stadium sealed European qualification.
It means Arsenal will not be playing European football next season for the first time since the 1995-96 season.
Spurs went into the final round of matches in seventh place but knew a slip-up at the King Power Stadium would open to door for Arsenal to leapfrog their north London rivals.
West Ham secured sixth place and a Europa League place by beating Southampton 3-0, leaving Tottenham and Arsenal to battle it out for a Europa Conference League spot.
Tottenham fell behind early on against Leicester when Jamie Vardy scored a penalty but Harry Kane equalised at the end of the first half and Spurs were still seventh at half-time.
Arsenal went ahead against Brighton through Pepe early in the second half and Vardy scored another penalty to put Leicester in front against Spurs, moving the Gunners up to seventh.
Pepe then put Arsenal 2-0 ahead with his second goal at Emirates Stadium.
But an own goal from Kasper Schmeichel drew Tottenham level at 2-2 and Bale scored twice late on to ensure Tottenham finished seventh.
The Europa Conference League will be the third UEFA club competition and will run alongside both the Champions League and Europa League.
Spurs will enter at the Play-Off round, which will a two-legged affair on August 19 and August 26. The Premier League season starts on the weekend of August 14.