The 29-year-old Spaniard will leave Ferrari at the end of the 2024 campaign after seven-time world champion Lewis Hamilton was announced as his replacement at the Italian giants earlier this year.
Sainz has won three F1 races so far in his career, the most recent at the Australian Grand Prix in March.
Having previously driven for Toro Rosso, Renault and McLaren, Sainz had been linked with several teams for the 2025 season including Alpine, Sauber and Mercedes.
But on Monday it was confirmed he had agreed an initial two-year deal at Williams, with an option to extend.
"I am very happy to announce that I will be joining Williams Racing from 2025 onwards," Sainz said in a team statement.
"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."
He added: "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, where many of my childhood heroes drove in the past and made their mark on our sport.
"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 will replace Logan Sargeant at Williams, where he will partner Alex Albon.
Founded in 1977 by the late Frank Williams, the team have won nine F1 Constructors' Championships and seven drivers' titles, with Alan Jones, Keke Rosberg, Nelson Piquet, Nigel Mansell, Alain Prost, Damon Hill and Jacques Villeneuve all crowned world champion while at Williams.
But Williams have struggled in recent seasons and last took a podium finish in 2021, while their last race victory came via Pastor Maldonado's shock win back at the 2012 Spanish Grand Prix.
"Carlos joining Williams is a strong statement of intent from both parties," said Williams team principal James Vowles.
"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 upwards trajectory we are on."
