By contrast, the 73-year-old O'Neill won seven out of eight games after being brought in as caretaker boss for eight games after Brendan Rodgers' exit in October.
O'Neill, a full-time manager of the Glasgow giants from 2000 to 2005, stepped aside for Nancy in early December.
But Nancy was sacked on Monday after just eight games in charge, including six losses.
"I am really pleased, in fact, very honoured to be asked back to manage the team again, and I am looking forward to getting back to work again with the players," O'Neill told Celtic's website.
"I know we would all have hoped for things to have worked out differently under Wilfried, and I personally want to wish him good luck with everything he does in the game. He is a fine man, and I am sure he will go on and achieve success again; I have no doubt of that.
"I've been asked to take this great job on again, and my focus will be to try and get us back to winning ways if we can. We will need everyone right behind us."
O'Neill returns with Celtic still second in the table, six points behind leaders Hearts, following a 3-1 loss at home to arch-rivals Rangers.
Defeat in the Glasgow derby sparked protests outside Celtic Park by frustrated fans and signalled that Nancy's time at the club was nigh.
And a club statement issued earlier Monday confirmed the end of the 48-year-old's brief reign.
"Celtic Football Club today announces that it has decided to terminate the contract of manager Wilfried Nancy with immediate effect," it said.
The Hoops added the Frenchman's coaching staff, and Paul Tisdale, the head of football operations, had also left the club.
Celtic interim chairman Brian Wilson said the way things had worked out for Nancy was "an intense disappointment, not least from a purely human perspective".
But he added the return of O'Neill meant Celtic could "look forward with confidence," explaining the former Republic of Ireland boss was a "manager the players, staff and supporters know well, with a peerless reputation in football and a deep commitment to Celtic".
'Kamikaze' Nancy
Nancy, previously in charge at MLS side Columbus Crew, started his job as Celtic manager on December 4, signing a two-and-a-half-year contract and taking over from interim boss O'Neill.
But the appointment quickly turned sour, with four defeats in his first four games, including a 3-1 loss to St Mirren in the Scottish League Cup final.
Nancy finally earned his first wins in late December, with Celtic beating Aberdeen and then Livingston.
But they lost to Motherwell and collapsed at home to Rangers, despite taking the lead at Celtic Park.
Former Celtic striker Chris Sutton compared Nancy's position to that of Ruben Amorim, sacked as manager of struggling English giants Manchester United just hours earlier on Monday, "but over a shorter period".
"He was fixated on changing Celtic's style, moving to a 3-4-3, playing one particular way," Sutton told Sky Sports News. "He just wasn't adaptable, and for Celtic to lose six and ship as many goals as they did -- it was kamikaze stuff from Nancy."
O'Neill's first game back in charge will be a Scottish Premiership fixture at home to Dundee United on Saturday.