The deal was signed at the Paris Air Show at Le Bourget Airport near Paris by MBDA chief executive Marwan Lahoud and Thomas Enders, the head of EADS's Defence division.
Financial terms of the sale were not disclosed.
EADS holds 37.5 percent of MBDA, while BAE Systems of Britain holds 37.5 percent and Finmeccanica of Italy holds 25 percent.
MBDA is the world's second leading missile manufacturer, after US company Raytheon, with sales of 3.1 billion euros (3.7 billion dollars) in 2004.