"Rubens needs no introduction," team founder Frank Williams said in a statement on Monday announcing his all-new line-up for 2010.
"He is not only the most experienced driver in Formula One but a passionate and talented driver who fought hard for the drivers' championship this year.
"Nico Hulkenberg won the GP2 Championship this season as a rookie and has previously won the F3 Euroseries, Formula Masters, A1 GP and Formula BMW Germany."
Hulkenberg was also the team's test and reserve driver this season.
Williams thanked departing German driver Nico Rosberg, the highly-rated 24-year-old who is expected to take Barrichello's place alongside Jenson Button at Mercedes-powered champions Brawn GP, and Japan's Kazuki Nakajima.
"Nico and Kazuki have represented Williams and our partners with dedication, discipline and skill and we wish them every success with their future endeavours," he said.
Toyota-backed Nakajima, son of former racer Satoru, ended the season in Abu Dhabi on Sunday with the unfortunate distinction of completing all 17 races without scoring a point.
Williams have already announced that they are switching to Cosworth engines from Toyota.
Rosberg, son of Finland's 1982 champion Keke, had already announced last week that he was leaving after four seasons with Williams.
Barrichello, who entered Formula One in 1993 before his close friend and compatriot Ayrton Senna died in his Williams at Imola in 1994, will be the first race-winner to drive for the team since Colombia's Juan Pablo Montoya and Germany's Ralf Schumacher in 2004.
Williams will be his sixth team after Jordan, Stewart, Ferrari, Honda and Brawn.
Williams have not won anything since 2004 but Barrichello, winner of two races with Brawn this season, said at the weekend that he hoped to be challenging for victories again next year.
"I am very hopeful of having a very competitive car next year, so that is what I want from myself. I want to go on and keep on winning," he told reporters.
"Everyone would look at a position at Williams, because it is one of the best teams out there and it is on the way up," added the Brazilian, championship runner-up to Michael Schumacher at Ferrari in 2002 and 2004.
The 37-year-old is Formula One's most experienced driver, with a record 285 races to his name and 11 victories. He is now on course to become the first driver to have started 300 grands prix.
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