"The government of the French Republic and the government of Iraq, wishes to promote and to reinforce the ties of friendship and cooperation existing between their two countries and two peoples."
The two countries, "on the basis of mutual respect for their sovereignty ... have taken the decision to re-establish diplomatic relations from 12 July 2004," the statement said on Monday.
Both "governments are convinced that this decision will contribute to a strengthening of links between France and Iraq and to an intensification of their exchanges, in the best interests of the two countries," it said.
The statement, issued by foreign ministry spokesman Herve Ladsous, said the two countries would exchange ambassadors "as quickly as possible".
Other news reports stated that interim Iraqi Prime Minister Iyad Allawi met with Bernard Bajolet, France's highest diplomatic representative in Iraq, and discussed the restoration of ties that broke off in 1991 during the Gulf war, a foreign ministry spokesman said.
"Mr Allawi said he wanted to do it as fast as possible so that France can participate in the reconstruction of Iraq," the spokesman said. "We welcomed that very positively."
France opposed the US-led war that invaded Iraq last year without UN authorisation and exercised its veto right in that regard.
It has also turned down US requests for military help in quelling an insurgency that threatens the interim Iraqi government.