Tevez has not played for the Premier League leaders since September after falling out with City boss Roberto Mancini following his refusal to warm-up during a Champions League defeat at Bayern Munich.
The Argentine star returned to his homeland soon after the bust-up and refused to return to Eastlands for more than three months.
But Tevez was unable to negotiate a move during the January transfer window, with potential transfers to AC Milan, Inter Milan and Paris Saint-Germain all falling through, and he finally flew back to England last week.
Mancini, who initially said Tevez was “finished” at the club, has maintained he would only consider the player for selection again after an apology, and the 28-year-old has now bowed to the Italian’s demand.
Tevez has also withdrawn his appeal against City’s fine of six weeks’ wages for gross misconduct, which was due to be heard by the Premier League in the coming days.
In a statement released by City on Tuesday, Tevez said: “I wish to apologise sincerely and unreservedly to everybody I have let down and to whom my actions over the last few months have caused offence.
“My wish is to concentrate on playing football for Manchester City Football Club.”
While away, Tevez had been found guilty of gross misconduct and City took a firm line over his potential sale.
Tevez, who had twice previously submitted transfer requests, was estimated to have lost £9.3 million ($14.7m) in wages or bonuses over various matters.
He failed in his initial appeal against the fine of six weeks’ wages for gross misconduct — thought to be around £1.2m — to the club board but lodged another with the Premier League.
His withdrawal of that appeal should now ease his return to action with the title-chasers.
Tevez sparked further controversy shortly before his return to the UK last week when he accused Mancini of treating him “like a dog” in Munich but that matter now also seems to be closed.
City’s statement read: “Carlos Tevez has today apologised to all concerned for his recent conduct.
“Carlos returned to the football club last Tuesday, following a three-month absence from duties, without permission.
“Carlos has also withdrawn his appeal against the club’s finding of gross misconduct, which was due to be heard by a Premier League panel in the coming days.
“He has since begun a training programme designed to return him to optimum fitness.”
Tevez was given his own fitness programme when he reported back to the club’s Carrington training headquarters last week.
He had said he could be match-fit in two weeks but it remains to be seen how quickly he can get himself back into first-team contention.
The former Manchester United and West Ham United forward is ineligible to play in Wednesday’s Europa League tie against Porto, having not been registered for the competition.
But he could feature for the Premier League leaders against Blackburn Rovers and Bolton Wanderers on February 25 and March 3.
City are currently two points clear of reigning champions Manchester United as they look to win the club’s first English title since 1968.
If Tevez can recapture the form that made him such a hit in his first two seasons with City, it would be a major boost to Mancini’s hopes of snatching the title away from Old Trafford.