The 30-year-old forward put pen-to-paper on a three plus one year deal with the Istanbul Giants.
The signing was unveiled by Galatasaray president Dursun Ozbek at the Ali Sami Yen Medya Center. Financial details of the transfer are yet to be disclosed by the club.
Podolski has been on holiday in Antalya, Turkey for the past week. The former Bayern Munich player who has a year remaining on his contract with Arsenal, had an unsuccessful spell with the Serie A giants scoring just one league goal
The 30-year-old won the World Cup with Germany last season and wants regular first team football to keep his place in the national team side.
Podolski scored three goals in 12 appearances for Arsenal last season. The Arsenal forward has scored 48 goals in a 125 international appearances.