The 29-year-old German has scored 31 goals in 82 appearances for Arsenal since arriving from Cologne in 2012.
"Everyone at Arsenal would like to wish Lukas the best for his time in Serie A," the London club said on their website.
This season the World Cup winner has been reduced to being a bit-part player at Arsenal despite injuries to Olivier Giroud and Theo Walcott, with manager Arsene Wenger appearing to better trust the speed and skills of younger players such as Danny Welbeck and Alex Oxlade-Chamberlain.
Podolski has made just two starts and 11 substitute appearances for the Gunners, netting three times, during the current season.
Podolski became the youngest ever European to reach the 100-cap mark for his country during Euro 2012.
(Writing by Pritha Sarkar, editing by Ed Osmond)
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