Brendan Rodgers has been appointed the new manager of Celtic on a 12-month rolling contract.
Deila delivered two league titles in as many years as Celtic secured a fifth successive Scottish Premiership success this season.
Rodgers has been looking for a new club since parting company with Liverpool in October after almost three-and-a-half years at Anfield.
The former Swansea boss led the Reds to seventh in the Premier League in his first season in 2012/13, one place higher than the previous campaign, and the following year Rodgers' side came within two points of being English champions for the first time in 24 years.
I have followed Celtic all my life and this is genuinely a huge honour for me.
Liverpool were lauded for their attacking play as they scored 101 league goals, while Rodgers was named LMA Manager of the Year.
The team dropped to sixth position the following season, and after a poor start to the 2015/16 campaign, Liverpool decided to replace Rodgers with former Borussia Dortmund boss Jurgen Klopp.
Rodgers is Celtic's third manager from Northern Ireland in recent years, with Martin O'Neill and Neil Lennon enjoying glittering spells while in charge of the club.
Speaking to the club's official website, Rodgers said: "I am absolutely delighted to be named Celtic manager. This is genuinely a huge honour for me. I have followed Celtic all my life and to be given this fantastic opportunity and to be part of such a truly great football club is a dream come true.
"I will give my new role everything I have and do all I can to bring our supporters exciting, entertaining and winning football. The club has been in magnificent shape in recent years and has collected silverware regularly during this time. My objective now, of course, is to continue this work, to keep us at the top and again make our mark in Europe.
"I know what a magnificent support Celtic enjoys and I can promise our fans one thing - that I will be doing everything I can to give you a team that you can be proud of and a team that delivers. I can't wait to be in Paradise with our team and our fans as we all get to work."
Celtic chairman Ian Bankier said: "We are delighted to welcome Brendan to Celtic as the club's new manager.
"As expected, there was huge interest in the position of Celtic manager but we believe we have chosen the outstanding candidate to take the club forward.
"Brendan is a man with a tremendous pedigree in football management. He is someone who knows all about Celtic and someone who has a real passion for Celtic. He is also a manager who we believe has the talent, the drive and the determination to bring continued success to the club.
"We are sure Brendan will receive a fantastic welcome from our supporters and we now look forward with real excitement towards next season as we tackle the many challenges ahead domestically and in Europe."
And chief executive Peter Lawwell believes the club has appointed a 'special manager' who will bring 'special times' back to Celtic Park.
He said: "Brendan is a highly sought after manager and we are pleased that we have been able to bring such a high calibre individual to Celtic.
"He has a huge and genuine affection for the club. I know Brendan feels privileged to be named Celtic manager and I know he will give us everything he has to be successful at Celtic. Above all, he will bring huge experience, knowledge and ability to the role.
"We wanted to bring one of the biggest and best names to the club to match our own aspirations and those of our supporters - we believe, in appointing Brendan, that we have done this. We have appointed a special manager and we are sure he can bring some special times to Celtic."
Rodgers will be officially unveiled at a media conference at 4pm on Monday at Celtic Park before meeting the supporters at the stadium two hours later.