Danone said it was offering $56.25 per share in cash in a deal that would double its U.S. business and was its largest acquisition since the purchase of Dutch group Numico in 2007.
The deal will boost the French company's pursuit of affluent consumers by adding WhiteWave's popular health food offerings such as Silk almond milk and Earthbound Farm Organic salad to its portfolio, as it struggles with setbacks in more challenging markets such as Brazil and Russia.
It is the first major transaction by Emmanuel Faber who took over as Danone's chief executive in 2014. He has vowed to return the French company to "strong profitable and sustainable growth" by 2020, reviewing its business in China and overhauling its dairy division where it has cut costs and launched new products.
The deal, which will be 100 percent debt financed and will boost earnings per share from the first year after closing, was approved by the boards of both companies.
It represents a premium of 24 percent over WhiteWave's 30-day average closing trading price, Danone said in a statement.
"This transaction will create a leading U.S. refrigerated dairy player, as well as one of the top 15 largest U.S. Food and Beverage manufacturers," it said.
After the deal, which is expected to close by year-end, Danone's North America footprint will increase to 22 percent of Danone's total portfolio from 12 percent.
The acquisition of WhiteWave comes as its shares hover near 11-month highs, buoyed by strong demand for the company's beverages, frozen desserts, yogurts, and milk and dairy products
Danone, whose brands include Actimel and Activia, competes globally with Nestle and Unilever.
CNBC contributed to this story