Rosberg has spent the last four years competing for Williams. Yet to win a race in 70 starts, the 24-year-old son of Finland's 1982 champion Keke finished seventh overall this season. His best finish is second place in Singapore in 2008.
Mercedes took over the British-based team last week, renaming it.
Brawn, who emerged from the remains of the Honda team, won both titles in their debut season but Britain's world champion Jenson Button [ Images ] has joined McLaren [ Images ] while Brazilian Rubens Barrichello [ Images ] has taken Rosberg's place at Williams.
"I am really happy to be a part of the Silver Arrows re-launch in 2010 as a driver for Mercedes," Rosberg said in a statement.
"I am more motivated than ever and can hardly wait to start testing with the new Silver Arrow and for the first race of the new season at Bahrain on 14 March," added the German, whose signing for the team was an open secret in Formula One circles.
Team principal Ross Brawn [ Images ] added: "Nico is a great talent and with four years of experience in Formula One is a driver who will be able to make a valuable contribution to our team right from the outset.
"I had the pleasure of working with his father Keke during his Formula One career and it is great to see Nico following in his footsteps."
Mercedes have yet to name their second driver, amid media speculation that seven-times world champion Michael Schumacher [ Images ] could be tempted out of retirement at the age of 41.
Finland's 2007 champion Kimi Raikkonen [ Images ], who has announced plans to take a year out after leaving Ferrari [ Images ], could be another option while Germany's Nick Heidfeld [ Images ] is available and seen as a safe pair of hands.