Rodgers won seven domestic trophies with the club during his first stint at Celtic Park, including an unbeaten season and consecutive trebles, before leaving to take over at Leicester in 2019.
"Celtic Football Club is delighted to announce that Brendan Rodgers has been appointed the club's new Football Manager on a three-year contract," Celtic said in a statement.
"Brendan previously managed the club to phenomenal success, winning consecutive domestic Trebles and in addition delivering the most famous of Invincible seasons."
The 50-year-old enjoyed a successful spell with Leicester, leading them to two fifth-place finishes in the Premier League and an FA Cup title triumph in 2021. However, he has been out of work since he was sacked in April, with Leicester later relegated on the final day of the season.
Celtic have been in search of a new manager after Ange Postecoglou left to take over as the new Tottenham head coach earlier this month.
"I am really delighted to return to Celtic and I am hugely excited by this great opportunity," Rodgers said. "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."