Rodgers’ departure comes with Celtic trailing Hearts by eight points in the Premiership after a 3-1 defeat at Tynecastle on Saturday.
The reigning champions host Falkirk on Wednesday before facing Rangers in Sunday’s League Cup semi-final.
O’Neill, who managed Celtic between 2000 and 2005, will be assisted by former player Shaun Maloney as club chiefs seek to appoint a permanent successor.
Rodgers, who began his second spell at Celtic Park in 2023, guided the club to consecutive league titles, adding to the two Premiership triumphs he achieved during his first stint in 2017 and 2018.
"Celtic can confirm that Brendan Rodgers has tendered his resignation. It has been accepted and Brendan will leave his role with immediate effect," a statement by the club said.
"The club appreciates Brendan’s contribution to Celtic during his two very successful periods at the club.
"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."
O’Neill, who won three league titles and reached a UEFA Cup final during his time in charge, returns to Parkhead nearly two decades after his departure.
Celtic are expected to consider several candidates for the permanent role, with Ange Postecoglou, currently out of work after leaving Nottingham Forest, among those likely to be approached.
Rodgers’ relationship with the club hierarchy had reportedly soured amid growing frustration over what could be viewed as a lack of ambition in the transfer market.