The Northern Irishman returns to Parkhead four years and four months after leaving for Leicester City.
Rodgers won seven trophies during his first spell as Celtic manager between 2016 and 2019, including the domestic treble twice.
He left Celtic top of the Scottish league table midway through the 2018/2019 season to take charge of Leicester City.
The former Liverpool and Swansea City boss replaces Ange Postecoglou, who left for Tottenham Hotspurs earlier this month.
Rodgers has signed a three-year contract.
Rodgers said on the club’s website: “I am really delighted to return to Celtic and I am hugely excited by this great opportunity. When I was given the privilege of being asked to join the club again, it was a very simple decision for me and my family.
“We have enjoyed some great times at Celtic before and this will be my goal again, to deliver good football, ensure we have a team we all love to watch and ultimately bring more success to our fans.
“Ange has done some brilliant work across the last two years and I will be doing all I can to maintain Celtic’s momentum as we face into all our domestic and European challenges.
“We have a hugely impressive and talented group of players and staff at the club, and I am really looking forward to meeting up with them all and then getting straight down to work.”
