"With a new manager and a new major shareholder, it feels very much like a new era here at Everton and that potential is what is most exciting," Walsh told the club's website (www.evertonfc.com).
"I know the club well, my roots are in the north west and my brother, Mickey, was an Everton player in the Bob Latchford era and always proud of that fact."
Walsh's departure will come as a big blow to Leicester manager Claudio Ranieri, who had already lost highly-rated scout Ben Wrigglesworth to Arsenal in February.
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Rob Mackenzie, another member of Leicester's recruitment team, was installed as Tottenham Hotspur's head of talent identification last year.
Ronald Koeman's Everton host Tottenham at Goodison Park in their opening game of the new Premier League campaign on Aug. 13.
(Reporting by Shravanth Vijayakumar in Bengaluru; Editing by Toby Davis)
