Ronny Deila is to leave Celtic at the end of the season, with the Premiership leaders saying the announcement was the manager’s decision.
It comes three days after a Scottish Cup semi-final defeat by city rivals Rangers at Hampden Park.
Deila, 40, told Celtic’s website: “There have been some disappointments and times when we have not achieved what we had hoped for.
“And I’m realistic and honest enough to admit that.”
Norwegian Deila, who arrived from Stromsgodset in his homeland in summer 2014, led Celtic to the title and League Cup triumph last season and his side currently lead the Scottish Premiership by eight points from Aberdeen with five games remaining.
But they have had two disappointing European campaigns and this season failed to reach the Champions League group stage and finished bottom of their Europa League section.
“It is vital that the club comes first and, instead of me being the focus, hopefully now the team and the club can be the focus as we enter this final important period of the season,” said Deila.
“It was an absolute privilege to be named manager of Celtic, such a wonderful football club, and I have enjoyed my time here immensely.
“There have been some great times and I am delighted that we have brought some trophies to the club.
“I was delighted in my first year to bring our fans a League and cup double and enjoy some European nights at Celtic Park and I am pleased this season to be well in contention to win another Premiership title.”
Deila said he now wanted to focus on securing a fifth title in a row for the Glasgow club.
Celtic chairman Ian Bankier said: “Ronny is a fine man with strong values of honesty and integrity.
“He has had some success, which we have enjoyed, and I know all our fans will back Ronny and the players as he looks to bring us more success in the shape of a second league title.
“We are all Celtic supporters and we all know that there can be disappointments in football, but I know Ronny is a man who has given his very best to the job and someone who will always care passionately about the club.
“The club, as always, will give Ronny our full support until the end of the season.
“We will then make a decision regarding our next manager with the objective of remaining Scotland’s pre-eminent club.”
Neil Lennon, who Deila succeeded at Celtic Park and recently left Bolton Wanderers, has immediately said he would welcome a return to the reigning Scottish champions.
Meanwhile, two former Celtic players – David Moyes, who recently left Real Sociedad, and Malky Mackay, last of Wigan Athletic – both refused to distance themselves from the job in recent weeks.
Celtic chief executive Peter Lawwell said: “Ronny has given everything to Celtic during the past two years and we thank him for his contribution to the club.
“He is a man of real humility, someone of tremendous character, and I personally wish him nothing but success for the future.”