The club revealed the Swede would leave Celtic Park at the end of the season to look at new challenges in football.
Mjallby said: “I have enormous affection for Celtic Football Club and it is with sadness that the time to leave has arrived. However, I now leave to seek some different opportunities.
“The club has been part of my life for almost two decades and I have been dedicated to them in every way, first of all as a player and then in management.
“I hope Neil, the staff and the players can deliver many more trophies and titles for our fans in the future.”
Lennon, who has been linked with the vacant manager’s job at Norwich, said: “I will be very sad to see Johan leave the club. He has given us such great service over a number of years and he will always be a big part of Celtic.”