Georgia had been contending with North Carolina for the film, which the governor's office says will bring about 250 jobs to the state.
The script is by novelist Nicholas Sparks, and Julie Anne Robinson will direct. Shooting is expected to begin in June.
Besides Savannah, the governor's office said the film will be shot at nearby coastal locations.
Cyrus, star of the "Hannah Montana" television series and films, will be playing another character this time.