Brandao, who spent two seasons with his former employers, also has an additional one-year option in his contract.
The 34-year-old forward hit 16 Ligue 1 goals in his time with Saint-Etienne, with Bastia set to become the third club he has represented in the French top flight.
After leaving Shakhtar Donetsk in 2009, Brandao moved to Marseille, where he netted 16 goals in 65 league appearances, before loan stints at Cruzeiro and Gremio in the Brazilian Serie A.
A brief return to Marseille followed before the striker moved on to Saint-Etienne.
Brandao will join up with Claude Makelele's squad as they look to improve upon their 10th-place finish last season.