Fourteen years after it was spun out from Johnson & Johnson, Waltham-based Alere Inc., a maker of medical diagnostics products, will be folded into another giant health care company.

Abbott Laboratories said Monday that it agreed to buy Alere for $5.8 billion, a vote of confidence in a company that has quietly grown into a global leader in devices used for so-called point-of-care tests performed at doctors’ offices, clinics, pharmacies, and patients’ homes.

Such tests, many of which can yield results in minutes, have become key tools in the shift of health care away from hospitals, and the business is expanding. Alere rang up sales of about $2.5 billion in 2015, and the purchase will give Abbott, already a big player in the field, annual diagnostic sales of more than $7 billion, or more than a third of its total revenue.

Abbott’s bid of $56 a share in cash represents a 51 percent premium over Alere’s closing price of $37.20 a share Friday, though the stock had fallen by a third from a 2015 peak of $55.99 in August. Abbott, based outside Chicago, also agreed to assume about $2.6 billion in Alere’sdebt.

Shares of Alere surged 45.4 percent to $54.10 on Monday. Abbott shares climbed 1.5 percent to $38.44.

“This is a great outcome for Alere and its people,’’ Alere chief executive Namal Nawana said in an interview. “What’s exciting is that Abbott is a great company that’s been around for over 100 years and has been in diagnostics for over 60 years.’’

The medical device industry has been consolidating, and there were two other deals announced on Monday. Stryker Corp., a maker of artificial hips and knees, agreed to buy Sage Products LLC for $2.7 billion in cash from its private equity owner, Madison Dearborn Partners. Medtronic PLC, the largest manufacturer of heart rhythm devices like pacemakers, agreed to acquire Bellco, a privately-held company that sells equipment for kidney dialysis. Terms of the deal weren’t disclosed.

Alere was spun off from health care conglomerate Johnson & Johnson in November 2001 as a separately traded public company called Inverness Medical Technology Inc. The company, rebranded as Alere in July 2010, built a diversified health care product line that included diagnostics, management services, and information technology.

When Nawana took the helm in 2014, he refocused Alere on rapid diagnostics, selling its management services unit Alere Health for $600 million to Optum, a health services arm of the insurer UnitedHealth Group, and divesting other businesses.

Nawana said Alere currently provides about 1.4 billion tests a year in more than 100 countries in everything from HIV to toxicology to cholesterol. “We pride ourselves on being very global and being relevant in each health care system around the world,’’ Nawana said.

Alere has nearly 10,000 employees worldwide, including more than 100 at its Waltham headquarters. While he said Abbott is expected to operate Alere as a subsidiary, Nawana said it hasn’t yet been decided whether he or others at the corporate office will remain with Abbott after the acquisition is completed. That is expected to happen by the end of 2016.

Abbott spokeswoman Darcy Ross said it was premature to comment on whether the buyer will retain the Alere brand or to detail plans to integrate the companies. Abbott has about 74,000 employees worldwide but does not have operations in Massachusetts.

“Alere has a strong management team and we look forward to ­working with them to build the premier point-of-care testing business,’’ Ross said in an e-mail. “We hope to keep the management team and ­employees.’’

In a conference call with stock analysts Monday morning, Abbott executives indicated that the bidding for Alere was competitive. They didn’t identify rival bidders.

“We think this is a great business with a complementary set of ­products that we’re going to be able to leverage in the marketplace,’’ ­Abbott chief executive Miles D. White told the analysts.

Material from Bloomberg News was used in this report. Robert Weisman can be reached at robert.weisman@globe.com. Follow him on Twitter @GlobeRobW.