Sixth in the constructors' championship, Williams use Toyota engines at present
Williams will be powered by Cosworth engines next season following the end of the team's links with Toyota.
Cosworth return to the sport in 2010 after a three-year absence, and will also supply engines for the four new teams - US F1, Campos, Lotus and Manor.
"Cosworth have impressed us," said Williams team boss Frank Williams.
"Working together, we will develop, not only a competitive racing car for 2010 but also a long-term partnership that can take on the best in Formula 1."
Williams, who lie sixth in the 2009 constructors' championship heading into the season finale in Abu Dhabi on Sunday, announced the long-term engine partnership with Cosworth on Friday.
Anyone would look at a position at Williams because it's one of the best teams out there, and they are on their way up
Frank Williams added: "Like Williams, Cosworth is an independent company whose owners share our passion for racing and engineering."
Cosworth is one of the most successful engine manufacturers to race in F1, and are second only to Ferrari in overall grand prix victories.
"Cosworth is delighted to be renewing our partnership with Williams," said Mark Gallagher, Cosworth's F1 general manager.
"We look forward to forging a long-standing relationship, not only for the supply of competitive Formula 1 engines, but also in the joint development of new technologies that have wider application outside of the sport."
The decision reignites old links between Williams and Cosworth.
The team took their maiden victory using Cosworth engines in 1979, their first world title in 1980 and used them until switching to Honda engines in 1984.
Brawn's Rubens Barrichello is strongly tipped to move to Williams next year, with present drivers Nico Rosberg and Kazuki Nakajima set to leave.
"I'm very hopeful of having a very competitive car next year," the Brazilian said on Friday, without confirming any move.
"Williams has always been a team that anyone would look at.
"That is no different right now. Anyone would look at a position at Williams because it's one of the best teams out there, and they are on their way up."
Meanwhile, US F1 have confirmed they will use the Motorland Aragon circuit in northern Spain as their European base when they make their debut next season.