The purchase will make Bayer the world's second-biggest maker of over-the-counter (OTC) or non-prescription products, it said.
"This acquisition marks a major milestone on our path towards global leadership in the attractive non-prescription medicines business," said chief executive Marijn Dekkers.
Merck & Co's consumer care business includes leading brands such as Claritin, Coppertone and Dr. Scholl's.
Pro forma sales of the combined businesses in 2013 amounted to $7.4 billion with Merck & Co's business contributing approximately $2.2 billion.
"With this transaction, we are acquiring leading product brands that will make Bayer the OTC leader in North America and Latin America and also move us into top global positions in key OTC product categories," said the head of Bayer's healthcare division, Olivier Brandicourt.
Bayer said the purchase price included a payment connected with sales of Claritin and Afrin in certain countries where these products were still prescription-only.
Bayer said it expected the integration of the businesses to generate significant economies of scale, for example in marketing spending and the cost of goods, "in the region of $200 million per year by 2017."
On top of this, rolling out Merck brands outside the US using Bayer's global infrastructure would generate revenue benefits of about $400 million by 2017.
Bayer said it anticipated one-time costs of approximately $500 million related to executing the transaction and combining the businesses, primarily in 2014/2015.
It would finance the acquisition with a bridge facility provided by Bank of America, Merrill Lynch, BNP Paribas and Mizuho.
The transaction was subject to approval from the relevant antitrust authorities, with closing expected in the second half of 2014, Bayer said.
Copyright Agence France-Presse, 2014