The German newspaper stated that an agreement has been reached after Arsenal boss Arsene Wenger failed to offer guarantees of regular first team football.
Germany national team manager Joachim Low revealed that he wants Podolski to play at least 30 to 40 games next season and this is believed to have influenced his decision.
Podolski will become the only Germany national team and World Cup winner in the current Galatasaray team.
Galatasaray have agreed personal terms with Podolski according to Eurosport TR on a deal worth €4.5 million per season (including bonuses) which puts him on par with Wesley Sneijder.
The Germany international striker currently earns €3.25 million per season at Arsenal.
Podolski won the World Cup with Germany last season and wants regular first team football to keep his place in the national team side.