No details were given about the length of the contract, although Renault said it is from 2010 onwards.
Kubica has driven for the BMW-Sauber team since 2006 while Alonso, one of the 24-year-old's best friends in the paddock, is moving to Ferrari [ Images ] next year.
The Pole won last year's Canadian Grand Prix [ Images ] and had been approached by several teams, including Toyota [ Images ] and Williams, once BMW [ Images ] announced they were quitting the sport at the end of the season.
"I am very happy I will be joining Renault in the 2010 season," Kubica said.
"I feel I have a special connection with this team because in 2005 I won the World Series by Renault. This gave me the chance to test with the team in Barcelona [ Images ], which led to my debut in Formula One.
"I share with Renault a strong winning mentality and feel comfortable with their friendly and open attitude," he added in a statement.
"I'm highly motivated and optimistic that together we can be at the front of the grid next year and, hopefully, fighting for the world title."
Former champions Renault are licking their wounds after a scandal-hit year, with the team handed a suspended permanent ban from the sport for their role in a race-fixing controversy.
Flamboyant former team boss Flavio Briatore has been banned for life and engineering head Pat Symonds barred for five years.
Kubica, an extremely quick and aggressive driver, has a no-nonsense style that will fit in well with the team's restructuring.
The tall Pole has also come up the hard way, with no family wealth to support him and from a country with no previous involvement in Formula One.
Although he had an impressive first test with Renault, he was snapped up by BMW-Sauber from under their noses as a test driver. He then replaced Canada's [ Images ] 1997 world champion Jacques Villeneuve as a race driver half way through 2006.
"Ever since Robert made his Grand Prix debut in 2006, he has been on our radar as one of the most naturally talented drivers of his generation," said Renault's acting team principal Bob Bell.
"He has delivered on that promise so it's great to have secured him in one of our cars next season. Renault has high ambitions and hopes for the future of the team and we feel that Robert can play a big role in fulfilling them."
Renault did not mention the second driver, currently French rookie Romain Grosjean.