The firm said it has agreed to acquire the remaining 39.9% minority interest in the Latapack-Ball beverage can business in exchange for six million Ball common shares.
The joint venture, established in 1995, supplies cans and ends to the Brazilian market from four manufacturing facilities.
Local business has grown over the years as customers' packaging mix continues to shift to metal beverage cans, said the firm.
John Hayes, chairman, president and CEO, said the move allows it to leverage, simplify and streamline business decision-making in Brazil and across the broader metal beverage business.
"By contributing their interest into a larger, global opportunity, our partners in Brazil will continue to participate in our future value creation as we better serve our dynamic customer base through increased supply chain efficiencies and optimization of Ball best practices to ensure that beverage cans are economically viable for years to come."
Ball bought a further 10.1% stake in the JV in 2010 to take its share past 60%.
The transaction is subject to customary approvals and is expected to close in the first quarter of 2016.
Ball said it will work with Brazil's Tribunal of Administrative Council for Economic Defense (CADE) to address any competition concerns regarding the proposed offer for Rexam.