The Germany international flew to Italy late last week to undergo a medical and finalise a deal which has now been confirmed by Arsenal.
Podolski has scored 31 goals in 82 games since joining Arsenal from Cologne in 2012, but he has started just twice this season following the arrivals of Alexis Sanchez and Danny Welbeck.
Podolski, who was part of the World Cup winning squad in Brazil during the??summer, has already linked up with Roberto Mancini’s Serie A side and trained in??Milan on Monday.
“He is experienced and has a wonderful career behind him,” said Mancini, the??former Manchester City manager. “He will help us and is not at the end of his career.”
The 29-year-old had already said his goodbyes to the club’s supporters, posting a message to his Instagram account over the weekend.
He said: “I can’t express in words my gratitude towards Arsenal fans for all they have done for me in my years in London!”
“Please know my heart always holds a place for you. I’ve loved every minute playing for Arsenal and I hope I have left my mark on the club and fans alike. Hopefully we shall meet again!”
Looking ahead to playing for the Nerazzurri, Podolski added:??”I’m (grateful) for the confidence the club has in me – and will try to pay it back with strong performances.
“I want to give a special thanks to coach Roberto Mancini who made a big effort for me to come to Inter, he made it an easy decision for me. I hope to rank among club legends like Ronaldo, (Javier) Zanetti, (Jurgen) Klinsmann, (Andreas) Brehme, (Lothar) Matthaus and many others one day.”