Diversified industrial company Danaher Corp agreed to buy medical diagnostics company Beckman Coulter Inc for $83.50 per share, or about $6.8 billion, including debt.

The deal represents an 11 percent premium to Beckman's closing price on Friday, and a roughly 45 percent premium over its price in December before rumors of a deal entered the marketplace, according to Beckman.

Beckman shares jumped 10 percent to $82.70 in premarket trading, while Danaher fell 10 cents to $47.88.

The transaction is valued at about $6.8 billion, including assumed debt, the companies said. The deal is expected to close in the first half of 2011.

Beckman Coulter, which has annual revenue of about $3.7 billion, would become part of Danaher's Life Sciences and Diagnostics segment.

Last December, sources told Reuters that Beckman had hired Goldman Sachs to weigh strategic options. The company makes diagnostic instruments used in medical testing systems.

Prior to that, Beckman had experienced a volatile year in which Chief Executive Officer Scott Garrett suddenly resigned after a high-profile recall of its troponin test and quality-control issues.

(Reporting by Lewis Krauskopf; Editing by Derek Caney and Lisa Von Ahn)