The 32-year-old Ivorian signed a deal at Anfield last month following a four-year spell with Manchester City.
Toure is now expected to fill the gap left by Carragher after the defender called an end to his 17-year career at the end of last season.
"It is a big honour," he told reporters. "To be chosen as Jamie Carragher's replacement is unbelievable.
"He has been a fantastic player for England and this football club, and is a great leader. It will not be easy but I will do my best."
Toure began his professional career with Arsenal in 2002 before joining City seven years later.