Danaher will pay Cepheid $53 per share in cash, a premium of 54 percent to its Friday close of $34.42, and the transaction is expected to close in the fourth quarter.
The company, which develops health care and environmental technology, said the addition of Cepheid would improve operational efficiencies and expand margins in its $5 billion diagnostics segment.
Sunnyvale, California-based Cepheid's GeneXpert systems enable genetic testing and provide test results for infectious diseases, among other clinical applications.
Danaher expects the acquisition to add about 30 cents to adjusted earnings in the fifth full year after the deal closes.
The equity value of the deal was $3.86 billion based on 72.9 million outstanding Cepheid shares as of June 30.
Fenwick & West is acting as Cepheid's legal adviser for the transaction, and Goldman Sachs is acting as Cepheid's financial adviser.
Cepheid's stock was up about 52.5 percent at $52.50, just shy of the $53 offer price in light premarket trading.