"Your main task will be to qualify the Lions for the 2013 African Nations Cup and the World Cup in Brazil in 2014. This contract is renewable," said Sports and Physical Education minister Adoum Garoua.
The minister said the contract runs until November.
Lavagne, the former coach of Cameroon champions Coton Sport, took over from Spaniard Javier Clemente who was sacked following Cameroon's failure to qualify for the 2012 Nations Cup, but was not a popular appointment.
Former Cameroon striker Roger Millar was among those who criticised the decision, labelling the 48-year-old from Beziers unqualified and set up a committee to try and unseat the football federation executive.
But FECAFOOT secretary general Tombi a Roko Sidiki said: "Denis Lavagne has met the main criteria of our federation which was looking for a coach who has been living in Cameroon and has full mastery of our championship so that he can select young local talent to fit into the national squad."
The signing of the contract on Monday came two days after Cameroon beat the Democratic Republic of Congo 1-0 in Yaounde at the start their World Cup qualifying campaign.
They next meet Libya on Sunday.
Lavagne has been in charge of six unbeaten games since taking over as coach.
In many African countries, the government employs national team coaches because the local football federation does not have enough money to pay them.