Appleton joined the Foxes as Craig Shakespeare's assistant last June before continuing the role under the former Southampton boss.
Jacques Bonnevay, most recently part of the Japan coaching setup, has now taken on the position ahead of the new Premier League season.
"I would like to take this opportunity to thank Michael Appleton for everything he has done to help me during his time with the club," Puel told the club's official website.
"He's a good man, a strong character and an excellent coach with the leadership qualities to continue building a successful career. We all wish him well in his future career."