The Argentinian had handed in a formal transfer request on December 11 which City rejected.
Now the club have revealed Tevez has expressed his "absolute commitment" and will be staying at Eastlands.
A statement on the club's website, mcfc.co.uk, said: "Manchester City can confirm to its fans that "clear the air" talks have been held with Carlos Tevez.
"During the meeting Carlos expressed his absolute commitment to the club and formally withdrew his transfer request.
"Carlos' contract remains unchanged and both Carlos and the football club are keen to focus on the opportunities that lie ahead."
Manager Roberto Mancini added: "Carlos is a world-class player whose contribution since he joined the club has been invaluable.
"I am pleased that we are now able to focus on pure football matters and to be able to look forward to Carlos continuing to play a significant role in the club's progress."