Flamini departed the Emirates Stadium to join Milan in the summer of 2008, but failed to establish himself with the Rossoneri and was released at the end of last season.
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But Wenger insists the 29-year-old's dedication to training and impressive attitude made him worth bringing back to north London, and says he is pleased with what he has seen so far.
“First of all I believe that he realised what he had here,” he told the club's official website. “When you're very young, it is difficult to understand what he had at Arsenal.
“He's got what is needed in every team. I wouldn't say we lacked that as much as people say but he is of course important for the balance of the team that we have players with his qualities.
“He is absolutely crucial to the balance of the team. He has done very well.
“He had not played since May and when you see how well he came in, it shows you how well, how focused and how dedicated he was in his preparation.
“I must say I was reluctant to sign him again but he was so honest in his statement that he wants to play the kind of football we play, that he wants to help us to win.
“He convinced me through his attitude and his desire in training that he will be the right signing for us.
“He could have gone somewhere else. He had offers but he wanted to put it right with this club and I think he felt somewhere that he had something to bring to the piece here. He was determined to do that.”