The Argentine striker also withdrew his appeal against a gross misconduct charge handed to him after he spent three months in his homeland without the club's permission.
"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," Tevez said in a club statement.
"My wish is to concentrate on playing football for Manchester City Football Club," added the 28-year-old, who has not played for City since refusing to warm up in September's Champions League defeat at Bayern Munich.
City manager Roberto Mancini, who after the events in Germany said Tevez was "finished" at the club, has previously suggested the striker could play again if he simply apologised.
With that apology now uttered, the question will be whether he will now get the chance to take part in the club's pursuit of a first league title since 1968.
He acknowledged last week he would have to be "brilliant" on the pitch to win over fans who burned shirts with his name on and having not played competitively for more than four months there are also question marks over his fitness.
City said the striker had begun a training programme "designed to return him to optimum fitness."
His prolonged and unauthorised absence prompted the club to fine him six weeks' wages after finding him guilty of gross misconduct for serious breaches of contract.
Tevez had lodged an appeal with the Premier League over the charge but has now withdrawn it, according to the club.
CHANGE GAMES
The return to Manchester and the apology are the start of the major bridge-building Tevez needed to do before any possible appearance in a sky blue shirt.
He did not help his cause last week when on the day of his departure from Argentina he accused Mancini of treating him "like a dog" in Munich and criticised his manager's handling of the entire situation.
Mancini rejected his accusations and said that if anything he had been too nice to the rebel forward.
However, the Italian has also said it would be better if Tevez was playing for the club as he was the sort of player who could change games.
The former City captain, whose work rate and goal-scoring prowess have never been in question, could make a return at a key part of the season.
Sitting two points clear of champions Manchester United at the top of the Premier League table with 60 points from 25 games, they might welcome the comeback of last season's joint top scorer for the title run-in.
