The 32-year-old joined City from Arsenal in a deal reported to be worth £16 million ($24.1 million, 18.7 million euros) in 2009 and was joined at the club by his younger brother, and fellow Ivory Coast international, Yaya Toure a year later.
Kolo Toure was initially installed as City captain, but he lost his place in the starting line-up after being handed a six-month ban for failing a drugs test in March 2011.
He claimed he had taken diet pills belonging to his wife and did not know they contained banned substances.
Despite his ban, he leaves City with FA Cup and Premier League winners' medals.
Kolo Toure's arrival at Anfield will provide Liverpool manager Brendan Rodgers with experience at centre-back, following veteran Jamie Carragher's retirement.