The 30-year-old was greeted by a large crowd of Galatasaray supporters. Galatasaray confirmed the news on their official website.
The Germany international is expected to put pen-to-paper on a three year deal with Galatasaray later today.
The Istanbul Giants will unveil the transfer at approximately 14:30 GMT at the Florya training facility.
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.