Goal understands the Frenchman has signed a two-year deal at the Emirates Stadium worth £50,000 a week, with his contract including an option for a third year.
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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 defence too. He is a very good addition to our squad."
Flamini won the FA Cup during his first spell at Arsenal as well as helping the Gunners reach the Champions League final in 2006, where they lost 1-0 to Barcelona.