The 35-year-old has been in Glasgow over the weekend to finalise the deal and watched on from the stands as his new team-mates lost on penalties against Leicester City in the International Champions Cup on Sunday.
Rodgers lured Toure to Anfield when in charge of Liverpool and expects the former Ivory Coast international, who has penned a 12-month contract at Celtic, to make his presence felt at the club.
"I brought Kolo into Liverpool to add that bit of experience and help to the centre-halves there at the time," Rodgers' told Celtic's official website.
"You saw from his impact there and in particular last season, he was a very important player for Jurgen Klopp towards the end of last season, playing in the Europa League final.
"He was outstanding in the big games for me when I was there. He looks after himself, he's a wonderful professional and he has good experience.
"With a lot of young players in our squad, he can really help them and he can be of great assistance for the likes of [club captain] Scott Brown, who is a wonderful leader.
"But he needs support and help around him as well. It will be nice for Scotty to have someone behind him who has that real big-game experience. Kolo can do very well for us."