Podolski will be transferred to Japan's J-League club Vissel Kobe for a fee of €2.6 million [$2.7 million] when the 2016-2017 season is over.
"Vissel Kobe will pay another €200,000 [$210,000] if Podolski manages to appear in 75 percent of the rest of the league matches and if the club manages to qualify for the Champions League's group or preliminary stages," said a statement on the club's official website.
Sharing his thoughts on social media, Podolski said his main focus is to help Galatasaray finish the season in a respectable spot.
"I can confirm that at the end of this season I will join Vissel Kobe from the J-League in Japan.
"It's not a decision against Galatasaray, it's a decision I made for a new challenge, and I will explain more when the time is right. But right now my only focus is helping Galatasaray and our fantastic fans!" he wrote.
Having joined Galatasaray from English club Arsenal in July 2015, Podolski was an influential figure in the team's 2015-2016 Turkish Cup championship.