Relegation-threatened Livorno have sacked Domenico Di Carlo after just 88 days in charge and re-appointed Davide Nicola.
Virgil van Dijk claims he knows nothing of interest from English clubs and is keen to prove himself in the Champions League with Celtic.
The 29-year-old, who made 153 appearances for the Gunners from 2004 to 2008, returns to the Emirates Stadium after five seasons in Serie A with AC Milan, having become a free agent earlier in the summer.
Arsenal manager Arsene Wenger is confident 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 at their Hertfordshire base this month.
"We are very pleased Mathieu has agreed to rejoin us," Wenger said on www.arsenal.com.
"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."