The Swede - who led England to the quarter-finals of the 2002 and 2006 World Cups and the last eight of Euro 2004 - takes over having left League 2 Notts County in February, where he had been director of football.
Former Russia and Chelsea coach Guus Hiddink had been strongly linked with the position before he becomes Turkey boss in August.
Ex-Blackburn and Manchester City manager Mark Hughes and former Real Madrid chief Bernd Schuster were also reportedly in the running for the Elephants' job.
"Eriksson signed a contract in London on Sunday," said Outtara Hego, secretary general at the Ivory Coast football federation.
"As most people know, Guus Hiddink was our first choice. When that did not happen, Eriksson was the best alternative. He has the necessary experience."
The FIF said it had considered several candidates since Bosnian Vahid Halilhodzic was sacked in February after failing to lead the team to the Africa Cup of Nations semi-finals.
"The executive committee analysed the profile of several candidates before choosing Sven-Goran Eriksson," FIF said.
"His mission will be to guide our team during the World Cup and to make sure it fares honourably, which will be difficult in a competition featuring the world's best 32 sides."
Ivory Coast have been drawn in World Cup Group G along with Brazil, Portugal and North Korea.
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