The Germany international will replace Bruma – who joined Real Sociedad on a year long loan – as the clubs number 11.
Podolski wore the number 9 jersey during his spell in the Premier League with Arsenal.
The 30-year-old signed a three-year contract with Galatasaray lsat week. The signing was unveiled by Galatasaray president Dursun Ozbek at the Ali Sami Yen Medya Center.
Podolski won the World Cup with Germany last season and wants regular first team football to keep his place in the national team side.
The Germany international scored three goals in 12 appearances for Arsenal last season. The former has scored 48 goals in a 125 international appearances.
Galatasaray won the Super Lig for the 20th time last season and earned the right to wear the fourth star next season.
The Lions booked a place in the Champions League group stages for the fourth consecutive season after winning the championship.