Massa and Bottas currently sit fifth and sixth, respectively, in the drivers' standings.
There had been speculation that Ferrari was interested in Bottas but that ended when Kimi Raikkonen renewed his contract with the Italian team two weeks ago.
"Stability is key for any team to thrive in Formula One, so to be able to enter a third season with one of the strongest driver lineups on the grid puts Williams in a fantastic position to continue its momentum towards the front of the grid in 2016," team principal Frank Williams said.
"(Williams) respect me a lot and the results are there," Massa said. "It has been so nice to be part of the big turnaround the team has seen since the end of 2013. I can't wait to carry on and continue pushing even more for the team, and for myself."
Bottas, a 26-year-old from Finland, had seven podiums over the last two seasons after coming through the team's development program.
"I believe we can achieve even stronger results than what we have seen so far," Bottas said. "I can't wait for 2016, however I am still fully focused on this season as we still have plenty of challenges to achieve."
"Felipe's blend of experience and raw speed is a rare attribute in Formula One," Williams said. "Felipe thrives in an environment where he is valued and can build a long-term relationship.
"Valtteri has become such a staple of Williams that we are as excited about the prospect of his potential as a championship contender as we are about returning the Williams name to the top of Formula One," the team founder added.
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