The move by both packaging giants marks part of an ongoing reorganisation in the market.
Companies are either moving to focus on profitable areas of the market, or, as in the case of Rexam, try to offer a range of packaging formats and materials to their customers.
Rexam recently sold off its glass bottle division for €660m to Ireland-based Ardagh in March this year.
Rexam has said it will focus on maintaining a lead in beverage cans and plastic packaging.
O-I Plastics, the division being purchased by Rexam, specialises in healthcare packaging and plastic tops.
The sale price excludes a tax accounting transfer to Owens-Illinois O-I Plastics is a US manufacturer of rigid plastic healthcare packaging and plastic closure systems.
The unit had sales of US$760m in 2006 and an underlying profit of US$114m. Rexam said it would give the company leading positions in healthcare packaging and closures.
"The acquisition will be an excellent fit in terms of customers, technologies, innovation, end use applications and geography," the company stated.
"The acquisition will offer significant value creation opportunities through cost and revenue synergies."
Leslie Van de Walle, Rexam's chief executive officer said the company expects the benefits will amount to about US$40m per year by 2010.
"The acquisition of O-I Plastics will transform our plastic packaging business and is consistent with our strategy to expand our positions in growth markets," he said.
"It gives us meaningful scale in plastics, leading market positions in core growth markets and is anticipated to create significant value through synergies and cross-selling opportunities."