O'Neill took charge temporarily five weeks ago after the resignation of Brendan Rodgers, and the 73-year-old's return to the club has brought four consecutive league wins to take them to within two points of leaders Hearts with a game in hand.
Celtic host Dundee on Wednesday, while Hearts are at home to Kilmarnock, and O'Neill has brought the club to within touching distance of the top having taken over when the side were eight points adrift of the leaders.
Media reports linking French coach Wilfried Nancy to the job had been circulating for the last couple of weeks, with speculation as to when O'Neill would step aside. The Northern Irishman announced his departure at the pre-match press conference.
"You will be relieved to know that this is definitely it for tomorrow evening," O'Neill told reporters.
"I have been assured by the board. The new man will come in, I'm not sure the terms of the process, but I know that this is definitely my last game."
O'Neill, who won three league titles and three Scottish Cups in his previous five-season spell in charge, made his brief return to management after more than six years since his last job, and has no qualms about his brief term coming to an end.
"That was the remit coming in to do it, whether it was going to last two weeks or five or six weeks," O'Neill said.
"That was always going to be the case so I have no complaints at all.
"A young gentleman's coming in and it's over to him, but we've got the big, big game here tomorrow evening and obviously, I'd like to try and win it if we can."
Nancy has spent his managerial career in Major League Soccer, with his first role coming at CF Montreal where he replaced Thierry Henry in 2021 and led the club to winning the Canadian Championship final before leaving for Columbus Crew.
At Columbus Crew, the 48-year-old has won both the MLS Cup and the Leagues Cup, and won the MLS Coach of the Year award in 2024. If, as expected, Nancy leaves the American club for Celtic, his first game in charge will be a home game against Hearts on Sunday.