The 28-year-old has signed a four-year contract with the Turkish side.
Juventus, AC Milan and Inter Milan has also been linked with the Brazilian in recent weeks.
Elano will cost Galatasaray around £8million, according to reports.
“Brazilian national football team player Elano Blumer (27) has signed a four-year contract with Galatasaray after playing at Manchester City for two years,” a brief statement read on the Turkish club’s website.
