The Brazilian joins from fellow Turkish club Sivasspor, having made a strong impression so far in his time in the country.
Robinho has scored eight goals for Sivasspor in the Super Lig this season, with only two players more prolific in the division in 2018-19.
Another former City man, Gael Clichy, is also at the club, although the full-back did not coincide with Robinho during his time at the Etihad Stadium.
Robinho joined Sivasspor from Atletico Mineiro in January despite being sentenced in absentia by an Italian court to nine years in prison just two months earlier.
He was found guilty of participating in an alleged incident of group sexual assault on a 22-year-old woman involving five other men in January 2013, although he has publicly protested his innocence.
The 34-year-old entered a not-guilty plea and denies the charges, with the case likely to be the subject of a lengthy legal process in Italy.
Robinho is a former holder of the British transfer record, having set City back £32.5m in 2008 upon leaving Real Madrid.
Despite a positive start in England, however, injury saw the striker fall out of City's plans, and in 2010 he returned to his first club Santos on loan.
Mixed spells with Milan, Guangzhou Evergrande and Atletico Mineiro followed before choosing Turkey as the place to reignite his professional career.