In 2014, it had sales of some 5.5 billion reals, or 1.2 billion euros at the current exchange rate.
Under the deal, JBS pays Marfrig $1.2 billion and assumes Moy Park's debt of about $293 million, the statement said.
JBS President Wesley Batista said the purchase will allow the company to broaden its product line and expand in the European market.
JBS is the world's biggest beef producer and a major poultry producer as well since the 2013 purchases of Tyson's operations in Mexico and Brazil, Marfrig's Seara subsidiary in Brazil and Frangosul, the Brazilian operation of France's Doux.
The group has nearly 200,000 employees worldwide and exports to 150 countries.