The UK-based household goods giant said the purchase would help it grow in China, and provide “a significant step forward” in its efforts to become a “leader in consumer health”.
Mead Johnson makes infant formula under the Enfa brand and had sales of $3.7 billion in 2016.
The deal is worth $17.9 billion once Mead Johnson’s debt is taken into account.
Mead Johnson chairman James Cornelius said Reckitt Benckiser’s offer provided “tremendous value” to shareholders.
They will receive $90 per share, 29% more than its $69.50 share price on February 1, before bid speculation began.
China’s 2015 decision to scrap its one-child policy could be an opportunity for consumer goods companies.
Couples are now allowed to have two children after concerns about China’s ageing population led the government to reverse the decades-long rule.
In 2016, China’s birth rate was the highest this century, with the number of newborns rising by 7.9% or 17.86 million in 2015.
As a result of this baby boom, analysts expect demand for food, formula, clothes and medicine to grow.
Reckitt Benckiser said it would fund the purchase with loans from its banks Bank of America Merrill Lynch, Deutsche Bank and HSBC, and through selling bonds.
The deal will need the approval of shareholders for both companies and regulators.
If Reckitt Benckiser shareholders reject the deal, the company will pay Mead Johnson $480 million.
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