The deal will result in an industry giant better equipped to withstand rising aluminum costs.
Rexam said its shareholders will get 407 pence in cash and 0.04568 new Ball share for each Rexam share held, amounting to 628 pence per share.
The offer was at a 17 percent premium to Rexam's Wednesday close. Ball's shares closed at $77.16 on Wednesday.
Ball Corp said in a statement that the deal valued Rexam at $8.4 billion including debt and would result in $300 million of achievable synergies by 2018.
A combination of the two largest beverage can makers by volumes would result in significant synergies. However, some analysts say the enlarged company would have to divest assets in the United States, Brazil and Europe to address antitrust concerns.
Rexam and Ball, suppliers to Coca-Cola Co and Anheuser-Busch InBev, each controls slightly more than a fifth of the market. Their nearest competitor, Crown Holdings Inc, has a 19 percent share, according to Vertical Research Partners.
Rexam shares rose 6 percent in early trading and were the top percentage gainers on the London Stock Exchange.