The 36-year-old featured 17 times for the Bhoys in all competitions last season, including nine times en route to their Scottish Premiership success.
As part of his new role, Toure will work with Celtic's football management team, supporting first-team coaching matters and working closely with Rodgers.
"This is great news for Celtic that we are able to bring a man of Kolo's experience into our coaching team," Rodgers told the club's official website. "In everything he does, he is quite simply a fantastic example to anyone."
Toure added: "I couldn't be happier to be back at this great club. This is a new chapter in my career, a new beginning. The football is over now. I can officially say I am retired from playing and now I am fully concentrating on coaching.
"For me there is no big change in terms of what I will be doing. I have always been the kind of player who tries to help those around me. Now I will try to give advice, help the young players and just guide them and pass on all the experience I have acquired during my career.
"I can learn so much from working with Brendan Rodgers, he is a top manager. I will be working with him and his staff very closely each day. He is one of the best young managers in the world right now. What he's doing for Celtic is there for all to see, he's doing amazingly right now."
Toure has also featured for ASEC Mimosas, Arsenal, Manchester City and Liverpool during his playing days, while representing Ivory Coast 120 times at international level.