The French carmaker said the team would remain branded Renault and preserve all the "core ingredients" that took it to the championships in 2005 and 2006.
But the cost for Renault would be cut in half, team managing director Jean-François Caubet told a news conference.
"The net cost that Renault had in 2009 and the net cost Renault has in 2010 will be divided in two," he said.
Renault declined to specify the size of the stake Genii was taking in its team but said it expected the deal to be completed in early 2010.
F1 team president Bernard Rey would only say it was a "significant stake".
Rey said the team would announce a new manager early next year at the same time as a second driver to partner Poland's Robert Kubica.
Renault, one of three manufacturers remaining in Formula One after the departure of Honda, Toyota and BMW in the last year, will continue to supply engines to the British-based team as well as this year's championship runners-up Red Bull.
"I am delighted to welcome Genii Capital as our new strategic partner as I am sure that their enthusiasm and business expertise will create a new dynamic for the team, the staff, and our partners," Rey said in a statement.
"Today's announcement also confirms Renault's commitment and trust in the sport's governing bodies to improve the green credentials of Formula One."
Rey said Renault intended to use the sport to show off the company's skill in developing high-performance, fuel-efficient cars.
Genii capital's chairman is Gerard Lopez, whose technology investment company Mangrove Capital was an early investor in Skype.
His main rival to take over the Renault team was the Prodrive company run by Aston Martin chairman and former Benetton and BAR team boss David Richards.
Genii said they would also "explore opportunities for synergies between companies in its investment portfolio and the Renault F1 Team."
"Formula One has an extraordinary level of global awareness that can be used to develop new business-to-business opportunities in traditional and developing markets, and there are exciting new revenue streams to be explored," said Lopez.