Podolski spent the second half of last season on loan at Inter Milan, but has now left the Emirates Stadium permanently after falling down the pecking order in north London.
The 30-year-old hopes to start a new and successful chapter at Galatasaray after failing to score a single goal for Arsenal during the first half of the 2014/15 Premier League season. His stint at Inter wasn't productive either, with the German scoring just one goal in 17 Serie A appearances.
"After good and open talks with Arsene Wenger I came to the conclusion that a change was the right decision," he told Sport Bild. "Galatasaray have tried very hard to get me for five years and in the end, the whole package fitted.
"The league is not at the level of the Premier League or the Bundesliga. But Galatasaray are a permanent feature in the Champions League and have stars such as Wesley Sneijder, who are world-renowned.
"Istanbul is a world metropolis and Galatasaray have a very good name in world football."
However, Podolski admitted that he plans to return to his hometown club of Koln for one final stint before hanging up his boots for good.
"When I have fulfilled my contract with Galatasaray completely, I'll be 34 years old," he said. "Every career will eventually come to an end, even mine. Still, I can well imagine that I will go on to Koln."