Everton have not visited Leicester since March 2004, when they drew 1-1. Marcus Bent's late equaliser cancelled out a Wayne Rooney strike from an Everton side reduced to 10 men following the dismissal of Duncan Ferguson.
The fixture will be played on the weekend of 16/17 August.
The following weekend, Roberto Martinez's men will take on Arsenal at Goodison Park and will seek to repeat the victory recorded over the Gunners in April, when Steven Naismith and Romelu Lukaku netted before a Mikel Arteta own goal made the final score 3-0 to Everton.
Other highlights from Everton's schedule include the Merseyside derby away to Liverpool in the sixth round of fixtures (27 September); the visit of champions Manchester City to Goodison on 10 January; and the return clash against Brendan Rodgers' Reds on 7 February.
Over the festive period, Everton will host Mark Hughes' Stoke City on Boxing Day, travel to face Newcastle two days later and then take on Hull City at the KC Stadium on New Year’s Day.
Everton’s 2014/15 campaign will end at home to Tottenham on Sunday 24 May.
Opening three games:
August 16 - Leicester (a)
August 23 - Arsenal (h)
August 30 - Chelsea (h)