"This acquisition marks a major milestone on our path towards global leadership in the attractive non-prescription medicines business," Bayer's Chief Executive Marijn Dekkers said in a statement on Tuesday.
Merck said it expects after-tax proceeds of between $8 billion and $9 billion from the sale, which is expected to close in the second half of 2014.
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"We can take these products and market them more forcefully than Merck has been able to do so far," Dekkers said in a conference call with analysts.
Bayer, the inventor of aspirin, has repeatedly said it wants to overtake J&J in the rankings.
Drug makers have embarked on a major reshuffling of their business portfolios. Novartis and GlaxoSmithKline (GSK) last month agreed to trade more than $20 billion worth of assets, while AstraZeneca is fighting off a $106 billion takeover approach from Pfizer.
Meanwhile companies including France's Sanofi, Merck & Co and Abbott are looking at selling off mature drugs that have lost patent protection.
OTC drugs units carry far lower margins than prescription drugs businesses but many drug majors regard them as attractive complements due to the stable stream of cash they can generate.
They akso require less spending on research and development and can be less exposed to the loss of patent protection where consumers remain loyal to a brand even when cheap copies become available.
But Reckitt Benckiser Group, one of the final contenders in Merck's auction, said on April 30 it was no longer in active talks to buy the Merck business, leaving Bayer in pole position.
Bayer also edged out other rival bidders, including Procter & Gamble Co PG.N, Boehringer Ingelheim, Novartis and Sanofi , people familiar with the matter have said.
J&J commands about 4 percent of the consumer health market - worth nearly $200 billion at the retail level.
Merck & Co has around 1 percent with brands including Dr Scholl foot care, Coppertone sunscreen and Claritin allergy medicine.
The fragmented OTC industry is consolidating fast. Novartis and GSK will form a joint venture in consumer healthcare as part of their agreement last month.
That deal would have relegated Bayer from second to third place in the global OTC rankings but the Merck deal will put it back on the second rung.
Reuters first reported last month that Bayer and Reckitt had emerged as frontrunners in the auction with each initially offering roughly $13.5 billion.
In addition, Bayer agreed to sell to Merck some rights to its Adempas drug against high blood pressure in the lung and other experimental cardiovascular drugs, saying it needed a marketing partner.
As part of that alliance, Merck will pay up to $2.1 billion, including $1.1 billion in milestone payments contingent on development achievements.
Bayer said it plans to finance the OTC acquisition with a bridge loan facility provided by Bank of America Merrill Lynch BAC.N, BNP Paribas BNPP.PA and Mizuho 8411.T, which will be syndicated to a larger group of banks.
It added no asset sales were needed to preserve its credit rating of "A-".
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