Toure, 35, joins Celtic on a one-year contract, the Scottish champions announced on Sunday.
Rodgers signed Toure for Liverpool in 2013, following the Ivory Coast player's previous spells at Manchester City and Arsenal.
After making him an early recruit in his Parkhead reign, Rodgers predicted Toure would thrive in Scotland and be a big asset to Celtic
Rodgers said: "I brought Kolo into Liverpool to add that bit of experience and help to the centre-halves there at the time
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."
Rodgers added on Celtic's website: "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 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."
Toure is relishing his spell in Glasgow, having experienced life previously in three of England's football hotbed cities.
He told Celtic TV: "I feel really excited because it's going to be a new challenge for me
I've come to one of the biggest clubs in the world and it's a privilege for me to be here
"I know a few friends who play football here and I know what the club has been achieving, winning a lot of trophies and playing Champions League a lot so that's something I'm looking at.
"I played with Brendan when he was at Liverpool and when we spoke about the chance for me to come here I was really happy because we know each other for a long time now
We've worked together and he's a top manager
For me it's a privilege to come and work with him again."
He added: "I have been playing for top clubs and I'm used to the challenge and I'm here to give everything I've got to win my place
You can only win your place on the pitch and that's through hard work, dedication and determination and I'm ready for that."
Source : PA
Source: PA