The Spaniard, who will be teammate to Alex Albon in place of US racer Logan Sargeant, is leaving Ferrari at the end of the year to make way for Mercedes' seven-time world champion Lewis Hamilton.
Former champions Williams said the winner of three races had signed a two-year agreement with options to extend.
"It is no secret that this year’s driver market has been exceptionally complex for various reasons and that it has taken me some time to announce my decision," said Sainz in a statement.
"However, I am fully confident that Williams is the right place for me to continue my F1 journey and I am extremely proud of joining such a historic and successful team.
"The ultimate goal of bringing Williams back to where it belongs, at the front of the grid, is a challenge that I embrace with excitement and positivity."
Sainz, who had also been of interest to Sauber/Audi and Renault-owned Alpine, said he was convinced Williams had "all the right ingredients to make history again."
Ferrari team boss Fred Vasseur, who was previously principal of Sauber and Renault before the French team rebranded as Alpine, said Sainz had made a good choice.
"I am pleased that Carlos will be joining Williams Racing from next season," he said in a statement.
"It's a team with a great history and legacy, founded by an enlightened man with an ambitious vision, so I know Carlos will feel at home there.
"I have great respect for (Williams principal) James (Vowles) and I am sure Carlos will make a valuable contribution to the team."
Alpine are considering switching in 2026 to the same Mercedes engines used by Williams while Sauber recently replaced principal Andreas Seidl with former Ferrari boss Mattia Binotto.
Sainz's decision makes it more likely that Italian rookie Andrea Kimi Antonelli will join Mercedes as Hamilton's replacement since they can no longer place him at Williams to learn the ropes as they did with George Russell.
Vowles previously worked at Mercedes under principal Toto Wolff, who is close to Vasseur despite their track rivalry.
"Carlos joining Williams is a strong statement of intent from both parties," said Vowles, describing the Spaniard as a perfect fit.
"Carlos has demonstrated time and again that he is one of the most talented drivers on the grid, with race-winning pedigree, and this underlines the upward trajectory we are on," he added.
"People should be in no doubt about our ambition and momentum as we continue our journey back to competitiveness - we are here, we are serious and with Dorilton’s backing we are investing in what it takes to return to the front of the grid."
Williams were dominant in the 1980s and 1990s but have not won a world championship since Canadian Jacques Villeneuve in 1997.
Sainz had been seen as the key to the driver market and now that the Spaniard has decided his future, the other seat announcements can follow.
