Massa, 32, joins from grid rivals Ferrari, for whom he has raced since the 2006 season, with Pastor Maldonado axed by Williams.
“The Williams F1 Team is delighted to announce that Felipe Massa will join the team to drive alongside Valtteri Bottas for the 2014 FIA Formula One World Championship season,” a team statement said.
“The new line-up reflects Williams’ determination to bring success back to the team,” added the statement, the marque having managed just a solitary point in the 2013 Formula One constructors’ championship with two rounds left.
Massa’s Grand Prix future was called into question when Ferrari announced they had re-signed Kimi Raikkonen for next season.
Massa has won 11 races and recorded 36 podium finishes in 12 seasons of Grand Prix racing.
He narrowly missed out on the 2008 drivers’ world title to Britain’s Lewis Hamilton by just a single point but helped Ferrari win the constructors’ world title in both 2007 and 2008.
Massa is currently eighth in the drivers’ standings for 2013, with Red Bull’s Sebastian Vettel having already wrapped up his fourth successive Formula One title.
“We are delighted to be able to confirm our 2014 driver line-up and welcome Felipe into the Williams family,” said team founder and principal Frank Williams.
“He is an exceptional talent and a real fighter on the race track; he also brings a wealth of experience as we begin a new chapter in our story.”
Massa said he was delighted to be joining another “iconic” team and one for whom Brazilian Grand Prix greats Nelson Piquet and Ayrton Senna had both raced.
“Williams is one of the most successful and important teams of all time in Formula One,” Massa said.
“When I was a kid, I always dreamed about racing for Williams, Ferrari or McLaren and I’m glad to be signing with another icon of the sport following my time at Ferrari.
“It is also nice to remember that some of the best Brazilian drivers raced for Williams and cemented a strong national link with the team.
“I hope my experience will be useful in helping the team in its effort to move on from a difficult period,” he added.
Bottas has yet to score a point in Formula One but Williams said he was heartened by the Finn’s recent performance in qualifying third in Montreal.
“Valtteri is a valued member of the team and I’m pleased he was able to demonstrate his talent in tricky conditions in Montreal.
“There is much more to come from him.”
Williams’ lone point of the season came courtesy of Maldonado’s 10th-place finish in Hungary but the Venezuelan, 28, could now find himself filling the vacancy at Lotus caused by Raikkonen’s move to Ferrari.
“The Williams F1 Team would like to take this opportunity to thank Pastor Maldonado for his efforts and contribution over the past three seasons, in particular delivering the team’s Spanish Grand Prix victory last year.
“We wish him well for the future,” the Williams statement said.
No Williams driver has won the world championship since Canada’s Jacques Villeneuve in 1997, the same year the team won the last of its nine constructors’ titles.