The City boss is set to meet with the Argentine forward on Thursday before allowing him to return to training with a view towards reinstating him to the first-team set-up
The City boss confirmed he had read Tevez's apology and that a meeting between the two was set for Thursday.
Speaking after City's 4-0 Europa League win over Porto, Mancini told ESPN: "I checked what Carlos said on his statement and tomorrow I will talk with him. I have accepted his apology."
Tevez spent much of the winter in his native Argentina following a highly publicised falling out with Mancini following the manager's accusation that the striker refused to warm-up for a game at Bayern Munich.
"I did say he was finished at the time," Mancini continued.
"But then one week after Munich I called him to my house and said ‘Carlos, apologise to everyone and this will be finished for me' - I don't have any problem.
"Yes, he can play again. I think he needs two or three weeks to train and play games of some sort but if he is in shape then of course he can be back."
The Citizen's cruised past Porto into the last 16 of the Europa league win, with Sergio Aguero scoring after just 19 seconds to set up a comfortable victory, which delighted Mancini.
"I think that we played a good game, it was difficult but we knew this before the game because Porto are a tough team," he added. "We won 4-0 and maybe this was too much but we won and we’re through to the next stage.
"It was good, it was important to score quickly but after Porto had lots of possession and we had to play with that."
Edin Dzeko and David Silva netted before David Pizarro rounded off the win with his first City goal and Mancini was delighted for his Chilean loanee.
He explained: "I’m happy for him, I know him very well because he was with me at Inter. I'm happy for him because he played 20 minutes and scored one goal, I think he can be a very important player for us with his quality and experience in the next two months."
The Italian also confirmed that he will continue to select full-strength sides for City's Europa League matches and reaffirmed his ambition to win the competition this season as well as the Premier League.
"If it’s possible, we want to be in the final," insisted Mancini.
"We know in the Europa League it will be difficult because there are tough squads, but we want to go in the final and for this reason we will play our best team.
"But we have 20 good players and we can make some changes for each game."