Leicester City have dropped into the Premier League's relegation zone following a 2-1 defeat to fellow strugglers Crystal Palace on Saturday.
Leicester have lost five of their last six Premier League games.
Rodgers spent four years in charge of the Foxes after being appointed in February 2019 and led them to their first FA Cup trophy in the 2020/2021 season.
Leicester finished fifth in each of Rodgers' first two full seasons in charge and reached the Europa Conference League semi-finals last season.
A club statement read: "Leicester City Football Club has reached a mutual agreement with Brendan Rodgers that will see him leave the club after four years as our men's first team manager.
"Brendan departs King Power Stadium as one of the most successful managers in the club's history, having guided us to our long-awaited first FA Cup triumph in 2021, the FA Community Shield in the same year, two of the club's three highest Premier League finishes and consecutive European campaigns, including our first European semi-final in 2022."
In a statement, Leicester's chairman Aiyawatt Srivaddhanaprabha said: "The achievements of the team under Brendan's management speak for themselves – we've experienced some of our finest footballing moments under his guidance and will always be grateful to him and his staff for the heights they helped us to reach on the pitch.
"Off the pitch, Brendan embraced the culture of the Club and helped cultivate an outstanding developmental environment. His place in Leicester City history is assured.
"However, performances and results during the current season have been below our shared expectations. It had been our belief that continuity and stability would be key to correcting our course, particularly given our previous achievements under Brendan’s management.
"Regrettably, the desired improvement has not been forthcoming and, with 10 games of the season remaining, the board is compelled to take alternative action to protect our Premier League status.
"The task ahead of us in our final 10 games is clear. We now need to come together – fans, players and staff – and show the poise, quality and fight to secure our position as a Premier League club."
Leicester are back in action against Aston Villa at the King Power Stadium on Tuesday.
