The centre-back's contract with City expired on Monday and the 32-year-old, whose move had been planned for some time, completed the formalities when the new transfer window opened.
Although Liverpool have not won the English league title for more than 20 years, Toure said he was thrilled to join the five-time European champions.
"This means a lot to me. Firstly, I'm joining one of the best clubs in England," Toure told liverpoolfc.com.
"I chose Liverpool because of the history and because of the spirit of the team and the people here."
Toure, who played alongside younger brother Yaya at City, is Liverpool's fourth major signing of the close-season transfer window.
He follows in the footsteps of Spanish forwards Luis Alberto and Iago Aspas and Belgium goalkeeper Simon Mignolet, all of whom reported to the club's Melwood training base for the first day of pre-season training on Tuesday.
Captain Steven Gerrard, who missed the end of last season due to injury, was also present, but striker Luis Suarez and goalkeeper Pepe Reina have been given extra time off due to their involvement in the 2013 FIFA Confederations Cup.