The midfielder has returned to north London after a spell with AC Milan and manager Arsene Wenger is happy to see his return.
The midfielder left the Gunners for AC Milan in 2008, making 122 appearances for the Serie A side before being released at the end of last season.
Manager Arsene Wenger says he is delighted that the Frenchman has returned to Arsenal, becoming the club's second signing of the summer alongside Yaya Sanogo.
“We’re very pleased Mathieu has agreed to re-join 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 defense too. He is a very good addition to our squad."