The French midfielder returned to England over the summer to train with the Gunners following his decision to run down his contract at AC Milan.
Wenger says he had no intention of putting terms to the 29-year-old at that stage, with Flamini having left the club five years earlier to take on a new challenge in Italy.
He was, however, able to convince Wenger that he was deserving of a deal, with Arsenal in need of combative characters in their engine room.
"First of all, I believe that he realised what he had here," said Wenger.
"When you're very young, it is difficult to understand what he had at Arsenal.
"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.
"It was his attitude. 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."
Flamini has been booked on both of his appearances this season, but Wenger will not be looking to change his game.
He added: "[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.
"He's got what is needed in every team."