According to Sky Sports, the decision comes after talks with major shareholder Dermot Desmond, who also held discussions with former Celtic striker Robbie Keane.
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O’Neill returned to the club on two separate occasions last season and led Celtic to a domestic double, including a Scottish Premiership title secured on the final day of the campaign.
After lifting the Scottish Cup at Hampden Park last month, O’Neill suggested the club may have been “looking at somebody younger” as they considered their next permanent appointment.
However, he will now remain in charge and is expected to continue working alongside his existing coaching team, including Shaun Maloney, Mark Fotheringham and Gavin Strachan.