Former Fulham manager Roy Hodgson has left Liverpool by mutual consent with Kenny Dalglish put in temporary control.
Hodgson left the Anfield club after winning just 13 of 31 matches in charge.
Principal Owner John Henry said on the club's official website: "We are grateful for Roy's efforts over the past six months, but both parties thought it in the best interests of the club that he stand down from his position as team manager. We wish him all the best for the future."
Hodgson said: "Being asked to manage Liverpool Football Club was a great privilege. Any manager would be honoured to manage a club with such an incredible history, such embedded tradition and such an amazing set of fans.
Liverpool is one of the great clubs in world football. I have, however, found the last few months some of the most challenging of my career.
I am very sad not to have been able to put my stamp on the squad, to be given the time to bring new players into the club in this transfer window and to have been able to be part of the rebuilding process at Liverpool.
The club has some great, world-class players, with whom it has been a pleasure to work and I wish the entire squad well for the rest of the season.
I thank those with whom I have built up a close working relationship at the club for their loyalty and support during very testing times, and finally of course to the Liverpool fans, your passion and dedication to the club will see Liverpool at the top of the game once more."
Club legend Kenny Dalglish will assume control of team matters for Sunday's third round FA Cup tie against Manchester United at Old Trafford.
Henry added: "We are delighted that Kenny Dalglish has agreed to step in and manage the team for Sunday's FA Cup tie at Old Trafford and for the remainder of the season.
"Kenny was not just a legendary footballer, he was the third of our three most successful managers - three giants. We are extraordinarily fortunate and grateful that he has decided to step in during the middle of this season."
Chairman Tom Werner said: "No one who cares for this great club has been happy with the way this season has unfolded and we have examined options and considered at length what is best for us going forward. Kenny will bring considerable experience to the position and provide management and leadership for the rest of the season."