The Hoops have already won th Scottish Premiership and the Scottish League cup with the Northern Irishman in charge.
“It just felt right. Myself, Peter and the board been talking for a little while and it felt the right thing to do,” Rodgers said after penning new terms. “I find it hard to find the words to express my feelings.
“We have a built a connection at the football club and that will be important going forward. A lot more to do and achieve, an exciting period for the club. Couldn’t be happier, in best place could possibly be. Eternally thankful to board for showing trust & commitment in me.
“A very easy decision, personally and professionally in a great place,” Rodgers added. “I’m a supporter who has got very lucky & someone who can hopefully develop the club further with the great people here.
“Beginning of journey. Only here a short time & want to grow an even greater connection between players & supporters. Hopefully the beginning of many more great times for supporters. Drive into morning at Lennoxtown & a real working environment & culture that I enjoy, everyone hungry to improve.
“Best we can be today but always one eye on tomorrow. Sit here with pride. A Celtic supporter that wasn’t good enough to play for team but next best thing is to manage it. Want to be here as long as I can. Celtic is the greatest club in the world and I have the privilege to manage it.”
Celtic Chief Executive Peter Lawwell could not hide his delight at securing the former Liverpool manager until June 2021.
“Brendan has made a huge impact at Celtic already,” Lawwell said in an official Celtic statement.
“He’s an outstanding manager and we believe he is one of the best coaches in Europe, if not world football, and we’re delighted that he has committed his future to Celtic.”
Rodgers’ side are unbeaten in 38 domestic matches, while he also guided the Bhoys into the group stages of the Champions League – drawing twice against Manchester City.