Liverpool sacked manager Brendan Rodgers on Sunday, with the decision coming just hours after a 1-1 Merseyside derby draw at Everton.
Rodgers, who almost guided the Anfield club to the Premier League title in the 2013-14 season, had been under growing pressure after an uncertain start to the season.
Liverpool are 10th in the Premier League, having taken 12 points from their first eight matches.
Club owners Fenway Sports Group are reported to have informed Rodgers of their decision in the aftermath of the draw at Goodison Park.
In a statement on their official website, Liverpool said the 42-year-old "will leave his post with immediate effect after having his contract terminated."
It said the process of appointing a successor was "under way" and "we hope to make an appointment in a decisive and timely manner."
Principal owner John W. Henry, chairman Tom Werner and president Mike Gordon said in the statement: "We would like to place on record our sincere thanks to Brendan Rodgers for the significant contribution he has made to the club and express our gratitude for his hard work and commitment.
"All of us have experienced some wonderful moments with Brendan as manager, and we are confident he will enjoy a long career in the game.
"Although this has been a difficult decision, we believe it provides us with the best opportunity for success on the pitch.
"Ambition and winning are at the heart of what we want to bring to Liverpool, and we believe this change gives us the best opportunity to deliver it."
Speaking after the game at Goodison, which saw Romelu Lukaku cancel out Danny Ings' opener for Liverpool, Rodgers had said he still felt "secure" in his job.
But the result means Liverpool have won only one of their past nine games and, after finishing sixth last season, are not currently on course to return to the Champions League.
Rodgers said at his postmatch news conference: "I have never been asked or told to deliver that by anyone at the club since I came in.
"I have never felt anything other than secure. That is not being complacent. I was brought here to do a job, I signed a new deal and the owners know it takes time.
"It will take time, whether that is me or someone else. While it is me, I will continue to devote every ounce to the club. People will want to put pressure on for different reasons. My job is to worry about the team -- that is the only pressure I will feel.
Former Swansea manager Rodgers, who took over from Liverpool legend Kenny Dalglish at Anfield in June 2012, did not win a trophy during his time at the helm.
He is the first Liverpool boss since the 1950s not to have won a trophy in his first three seasons in charge.
His overall record saw him win 83, draw 40 and lose 42 of his 165 games at the helm, but he won only four of 11 in all competitions this season despite spending around £80 million on new players in the summer.
Ex-Borussia Dortmund manager Jurgen Klopp and former Real Madrid coach Carlo Ancelotti are among the names to have been linked with the Anfield job.