Rodgers was given his marching orders just hours after his team drew 1-1 at Everton in the Merseyside derby to stand 10th in the English Premier League standings with 12 points from eight games.
The 42-year-old Rodgers took Liverpool to the brink of its first English title in 24 years in the 2013-14 season before losing out to Manchester City.
But with star player Luis Suarez departing to Barcelona, Liverpool could only finish sixth last season and finished it with a disastrous 6-1 defeat at Stoke.
Results in the current campaign have been patchy despite an outlay of nearly $450 million on players, with signings such as Mario Balotelli failing to make an impression.
An announcement on the club's official website sealed Rodgers' fate after three and a half years in charge, the Northern Irishman having initially been given the news in a phone call.
"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," Liverpool's American owners Fenway Sports Group (FSG) said in a statement.
"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."
FSG is an American sports investment company owned by John W. Henry and chaired by Tom Werner. The pair took over Liverpool in 2010 from previous owners Tom Hicks and George Gillett, while FSG also owns Major League Baseball side the Boston Red Sox and the home stadiums of both teams.
Rodgers, who arrived from Swansea City in 2012, gained accolades for the expansive football which Liverpool played in coming so close to adding to its tally of 18 top-flight titles in England.
Suarez and Daniel Sturridge helped them score over 100 goals, but a costly slip by captain Steven Gerrard in a 2-0 defeat to Chelsea left the team agonizingly short.
Gerrard and England international Raheem Sterling left Liverpool at the end of last season and Rodgers has struggled to find the right formula with their replacements.
"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," the statement added.
"The search for a new manager is under way and we hope to make an appointment in a decisive and timely manner."
Former Borussia Dortmund coach Jurgen Klopp and Italy's Carlo Ancelotti are the early reported favorites to take over at Anfield.
Earlier Sunday, there was another managerial departure in the EPL as Dutchman Dick Advocaat stepped down at Sunderland with the north-east club second bottom with three points from eight games.