The former England international hung up his boots at the end of last season to take up a career as a television pundit, which resulted in Brendan Rodgers snapping up the Ivorian from Manchester City.
"I am used to competition. When I came into Arsenal the competition was Sol Campbell, Martin Keown, Tony Adams - it was hard competition," Toure told the club's official website. "The only way to improve a team is to make players fight for their place.
"I know Jamie Carragher left the club and that's the reason why I'm here. He was massive for this club, he was a great professional and a great example for me.
"I will try to do what he did but I think that's going to be really difficult. It adds pressure because it's always hard to replace a big, big player like Jamie. I'm looking forward to that because I like challenges. I like to lead when I'm on the pitch, I like to speak to the players and organise things."
Toure spent four years at Manchester City.