Arsenal boss Wenger: Flamini has plenty of football ahead of him
Wenger is confident the versatile Flamini - who played at left-back in the 2006 Champions League final defeat to Barcelona - will settle quickly into life back at his old club, having spent some time training with the team this month.
"We are very pleased Mathieu has agreed to rejoin us," Wenger told the club's official website.
"He is a player of real quality, with a fantastic work rate and great mentality.
"As we know, Mathieu is a strong midfielder, but is also is comfortable playing in defence too. He is a very good addition to our squad."
Wenger added: "He is a bit older, but he is still only 29. The best years are in front of him now - the next three years.
"Physically, he is perfect. He was tested, prepared and he is physically in fantastic shape.
"He knows how we play football, knows the club and had a huge desire to come back.
"He was available because he was out of contract and he is a quality player, and a focused player. Those were all the reasons that pushed me to make that decision."
For the big stories and the banter follow us on Twitter: @tribalfootball