The club say a process to appoint a new manager is underway.
In a joint Fenway Sports Group statement, Principal Owner John W Henry, Chairman Tom Werner and President Mike Gordon said:
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.
The search for a new manager is underway and we hope to make an appointment in a decisive and timely manner.