Eriksson, who has been out of work since leaving his role as director of football at Notts County in February, had recently been interviewed for the Nigeria job but lost out to fellow Swede Lars Lagerback.
However, Eriksson was viewed as the best candidate for Ivory Coast after Russia boss Guus Hiddink decided to take the Turkey job.
Outtara Hego, secretary general at the Ivory Coast football federation, said: "Eriksson signed a contract in London on Sunday.
"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."
Eriksson's agent, Athole Still, told Soccernet on Sunday night: "Sven is here sitting beside me having just signed the contract and I can tell you he is very happy.
"He's only just signed the contract and I think the president made the announcement just before he signed it!"
He added: "I'm sure he would love his new team to play England and, if that was the case, he would only have one thought: to get the win.
"It would also mean that he would have got the Ivory Coast out of the 'group of death' with Portugal, Brazil and North Korea. After what happened to him with England, I am sure he would like nothing better than revenge over both Portugal and Brazil."
In an official statement, the federation said: "Aware of the great expectations of our population who have taken a keen interest in the matter, the executive committee focused its choice on Mr Sven-Goran Eriksson.
"The Swede has been, among others, coach of England and Mexico. He is an experienced technician who has been proven.
"His mission is to lead our team during this World Cup, and to ensure that there is an honourable participation in a competition reserved for the top 32 football nations in the world, and it obviously will be difficult.
"Therefore, the executive committee of the FIF appeals to the sacred union between the Elephants and their coach."
It was reported this week that Eriksson was on a three-man shortlist for the role along with former Manchester City boss Mark Hughes and former Real Madrid coach Bernd Schuster.
Eriksson led England from 2001 to 2006 and managed the team at three major tournaments, reaching the quarter-finals at the 2002 and 2006 World Cups as well as Euro 2004. More recently, he took charge of Mexico during the World Cup 2010 qualifiers but left the position after disappointing results.
At club level, he has managed sides such as Benfica, Roma, Fiorentina, Lazio and Manchester City, and has won trophies including the UEFA Cup, Cup Winners' Cup and Serie A.
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