Merck said that it aimed to establish "one of the leading players in the $130 billion global life science industry" through the purchase.
Merck will pay $140 per share in cash, adding that it expected annual synergies of about 260 million euros to be fully achieved within three years after closing the deal.
"The combined company will be able to serve life science customers around the world with a highly attractive set of established brands and an efficient supply chain that can support the delivery of more than 300,000 products," the two companies said.
Sigma-Aldrich is based in St Louis and employs some 9,000 people.
The purchase is expected to be closed by mid-2015 subject to regulatory approval.
Copyright Agence France-Presse, 2014