The 32-year-old Massa will partner Finnish driver Valtteri Bottas next season after being released by Ferrari following eight seasons driving for the Italian outfit.
Massa follows in the footsteps of Brazilian drivers Ayrton Senna and Rubens Barrichello, who both drove for the British team.
Massa has 11 race wins in his career, which includes two seasons at Sauber, and finished second in the 2008 world championship to Lewis Hamilton by a single point.
Massa says: "I hope my experience will be useful in helping the team in its effort to move on from a difficult period," with Maldonado having earned Williams' lone point this season.
The Venezuelan driver leaves after three seasons with Williams.