The Northern Irishman tendered his resignation, which was accepted by club chiefs, with Celtic eight points adrift of Hearts in the Scottish Premiership.
Martin O’Neill and Shaun Maloney will take charge of first-team matters in the interim period with a process to appoint a new manager underway.
A club statement confirmed: “Celtic Football Club can confirm that football manager Brendan Rodgers has today tendered his resignation.
“It has been accepted by the Club and Brendan will leave his role with immediate effect.
“The Club appreciates Brendan’s contribution to Celtic during his two very successful periods at the Club.
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“Brendan leaves Celtic with our thanks for the role he has played during a period of continued success for the Club and we wish him further success in the future.
“The process to appoint a new permanent manager is underway and the Club will update supporters further on this as soon as possible.
“We are pleased that during this interim period former Celtic manager, Martin O’Neill and former Celtic player, Shaun Maloney have agreed to take charge of Celtic first-team matters.
“Further details will be confirmed shortly.”
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