Ramsey played alongside Podolski for the last three years at the North London based club.
The 30-year-old Germany international signed a three-year contract with Galatasaray over the weekend in a signing ceremony held at the Ali Sami Yen Medya Center.
The World Cup winner has the option to extend his contract by a year if he makes over 30 appearances for the Lions during the 2018-19 season.
Podolski will also receive a €20,000 bonus for every appearance he makes. The Guners will receive at least €2.5 million from the Istanbul giants as part of the transfer fee.
The experienced striker won the World Cup with Germany last season and has scored 48 goals in a 125 international appearances.
The former Arsenal man has joined the Galatasaray camp after spending the last week on holiday in Antalya.