
The Reds drew with Everton on Sunday to leave them 10th in the Premier League and six points off the top spot.
“Although this has been a difficult decision, we believe it provides us with the best opportunity for success on the pitch,” said a club statement.
“The search for a new manager is underway and we hope to make an appointment in a decisive and timely manner.”
Rodgers, who took over in June 2012, led Liverpool to second place in the 2013-14 campaign, when they led the title race with three games to go but lost out to Manchester City.
The Northern Irishman was informed within an hour of Sunday’s 1-1 draw at Merseyside rivals Everton.