Rodgers has led Leicester City to an impressive start to the season that sees them second on the league table with 35 points from 15 games.
The Foxes have surprisingly emerged as unbeaten leaders Liverpool’s nearest challengers as they are eight points adrift top spot.
Rodgers joined Leicester City from Scottish champions Celtic in February, replacing Claude Puel in the process.
The 46-year-old Northern Irishman fueled talks of a potential move to managerless Arsenal earlier this week when he confirmed a break clause in his contract at Leicester.
Rodgers has however reiterated his happiness at the 2015/2016 Premier League champions by committing his future to 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 the chairman, Khun Top [Aiyawatt Srivaddhanaprabha]; from the chief executive, Susan Whelan; from the director of football, Jon Rudkin; and 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 matched a club record of seven straight league wins by beating Watford in midweek and will look to make Aston Villa their latest victim when they meet at Villa Park on Sunday.
