Podolski's agent had told Bild on Friday that the Germany international had decided to leave Arsenal after failing to receive assurances from Arsene Wenger over first-team football.
The 30-year-old, who had a disappointing loan spell at Inter Milan earlier this year, had already said he was considering a move to Turkey and Gala announced on Saturday morning that the deal would be completed later in the day.
Podolski is set to sign a three-year deal with Galatasaray after completing a medical.
The Turkish club would pay €4 million to release the forward from his Arsenal contract.
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