The 27-year-old joined Jaguar in 2003 from Minardi and will continue driving for the team for the rest of this season.
Williams will lose Ralf Schumacher, currently injured, and Juan Pablo Montoya at the end of the season.
"The deal I have agreed with Williams today really is the most significant milestone in my career to date, and I have great expectations of what we can achieve together," Webber said in a statement.
"Besides having an amazing history of success, the team has a reputation for a no-nonsense and straightforward approach to racing, which suits me just fine."
No details were given of the length of Webber's contract although Williams said it reflected a "long-term" mutual interest between the driver and the team.
"Mark is self-evidently a highly talented driver," said team boss Frank Williams. "But his tenacity, determination and motivation are also qualities we prize at Williams."
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He finished sixth at last weekend's German Grand Prix and qualified second alongside Michael Schumacher's Ferrari in Malaysia in March.
"Mark has now reached a stage where he needs to continue his progress and pursue race wins. We understand his decision and respect it," said Jaguar managing director David Pitchforth.
Ralf, brother of world champion Michael, will move to Toyota next season while Colombian Montoya leaves for McLaren after a disappointing season for Williams.
They have scored 47 points and lie fourth in the constructors' table.
Webber's move was announced shortly after Renault said Italian Giancarlo Fisichella would join their team from Sauber.