Appointed City’s manager in February, the former Liverpool and Celtic boss has enjoyed a successful start to his Leicester career.
City, which was crowned Premier League champion in 2015-2016, has won 17 of the 26 matches in that competition since Rodgers's appointment, moving it to second on the table after equalling a 56-year-old club record of seven consecutive top-flight victories.
Foxes chairman Aiyawatt Srivaddhanaprabha said: “Brendan’s qualities as a coach are well-known and evident in the way he has sought to unlock the potential in every member of our exciting young squad.
“But just as important to us is the suitability of Brendan’s wider philosophy to the club’s established culture and values. He and his staff immersed themselves immediately, building an understanding for the club and the city and an appreciation for what makes them special.
“That has been a valuable combination over the last nine months — strengthening the bond between our players, staff and supporters — and I’m excited to see how it can continue to enhance our long-term vision for the club.”
Rodgers said: “When I made the decision to come to Leicester City, it was because I was excited about the direction the club was taking and how I could apply my experience to the journey. I came here with a purpose to add something to that and to help the club build for the future.
“The support I have had from ... everyone at the club has been amazing. I’ve inherited an outstanding team of staff that are dedicated to progress and improvement and we have a group of players that are a joy to work with every day.
“And to the club’s supporters, I can only say thank you for welcoming me and my staff into your club and for putting your faith in our work. We’ll continue to work together to bring success to Leicester City for many years to come.”
Leicester City’s Premier League campaign continues on Monday (AEDT) when the Foxes travel to Villa Park to face Aston Villa.