Johnson Johnson said on Wednesday that it had agreed to buy the medical equipment maker Synthes for $21.3 billion in cash and stock, in one of the biggest deals ever in the health care sector.

Johnson Johnson is offering 159 Swiss francs ($181.30) a share for Synthes, a Swiss-American company that manufactures bone implants and surgical tools, and specializes in treatments for trauma.

The bid is comprised of 55.65 francs in cash and 103.35 francs worth of Johnson Johnson common stock. It represents a 22 percent premium over the 130.60 francs that Synthes was trading at on April 14, before reports of the deal first emerged.

“It’s a pretty fair price,” said Lisa Bedell Clive, an analyst at Sanford C. Bernstein in London. “For J.J. it’s a great deal. Trauma is one of the few med-tech markets where they haven’t had a top-three business.”

Both companies’ boards have unanimously approved the transaction, and a group of shareholders, led by the Synthes founder and chairman, Hansjörg Wyss, and other directors, have pledged to vote their shares in support of the deal, the companies said.

Mr. Wyss controls 47 percent of Synthes, a stake that will be worth slightly more than $10 billion when the deal closes. In the companies’ statement, he said he was pleased to see his “life’s work will continue as part of Johnson Johnson.”

His support for the deal, combined with the size of his stake, make it unlikely that shareholders pushing for a higher price would be able to block the bid.

“All the shares we have are totally in favor of the transaction,” Mr. Wyss said during the conference call.

Synthes will be merged with the Johnson Johnson unit DePuy Companies to become the group’s largest medical devices business, specializing in orthopedics.

“Orthopedics is a large and growing $37 billion global market and represents an important growth driver for Johnson Johnson,” William C. Weldon, head of Johnson Johnson, said in the statement.

The deal, which will be Johnson Johnson’s largest ever, is expected to close in the first half of next year, pending the approval of regulators in the United States and Europe, as well as Synthes shareholders.

In acquiring Synthes, Johnson Johnson will be combining the second- and third-largest businesses for spine-related implants worldwide, which could draw the attention of regulators and require a divestment.

“Antitrust authorities look at this on a product line by product line basis,” Ms. Clive said. “It could happen that they’ll let this go untouched,” she added.

“We don’t believe that there will be any required divestitures,” Alex Gorsky, vice chairman for Johnson Johnson, said during a conference call, “but if there are, we don’t think they will material-impact the transaction.”

The deal is set to have a “modestly dilutive impact” on Johnson Johnson’s earnings per share, the company said.

Johnson Johnson hired Goldman Sachs as its financial adviser, and Cravath, Swaine Moore as counsel, while Synthes hired Credit Suisse as adviser, and Shearman Sterling as counsel.

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