It was announced last month that the Ivorian has agreed a switch to Anfield, but he was unable to sign a contract with the Reds until his deal with Manchester City had expired.
That happened yesterday and so he has now penned a two-year contract with Brendan Rodgers's team.
"This means a lot to me. Firstly, I'm joining one of the best clubs in England," he told the club's official website.
"When I left City it was important for me to stay in England because it's the best league and to join Liverpool is massive for me.
"I chose Liverpool because of the history and because of the spirit of the team and the people here."