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Broadcom, the semiconductor giant, said on Thursday that it had agreed to buy the software company VMware in a transaction valued at $61 billion. The deal would furnish Broadcom with popular computing tools used by a large swath of corporations and reshuffle the vast market for enterprise computing technology.

The chip company will spend the equivalent of $138.23 per share for VMware in the cash-and-stock deal, it said in a statement. That is more than 40 percent higher than VMware’s stock price before rumors of a deal began to circulate over the weekend.

The combination would make Broadcom a significant player in data-center technology and cloud computing. It would also be the world’s second-biggest proposed acquisition this year, according to data from Dealogic. (Microsoft’s $75 billion bid for Activision Blizzard is the biggest.) VMware has more than 500,000 customers around the world, and counts as partners all the major cloud providers, including Amazon, Microsoft and Google. That makes VMware a prized asset for Broadcom’s chief executive, Hock E. Tan.

Mr. Tan had been one of the most acquisitive forces in the chip industry, stitching Broadcom together one deal at a time, until President Donald J. Trump blocked Broadcom’s proposed $117 billion takeover of the chip maker Qualcomm in March 2018 on national security grounds. Broadcom, which was based in Singapore at the time, has moved its headquarters to San Jose, Calif.

Since then, Mr. Tan has diversified his targets. He bought the software company CA Technologies for $18.9 billion later in 2018 and a security division of Symantec for $10.7 billion in 2019.

With its so-called virtualization software, which allows one computer to act like many machines and essentially makes computing more efficient, VMware would be Broadcom’s flagship asset. VMware reported revenue of $12.9 billion in its last fiscal year, which ended Jan. 28. That was a 9 percent increase from the previous year. That growth rate was much slower than the cloud-computing arms of Amazon, Microsoft and Google. Founded in 1998, before the cloud boom, VMware has depended on clients that still operate their own data centers.

A deal would be the latest in a series of major changes for VMware. The company, based in Palo Alto, Calif., lost its longtime chief executive, Pat Gelsinger, to Intel in January 2021. On May 12, it gained a new chief executive, Raghu Raghuram, and lost a chief operating officer, Sanjay Poonen, on the same day. In November, the software maker became independent when it was spun off from Dell Technologies.

Under Mr. Gelsinger, VMware was eager to extricate itself from the personal computer maker that owned a majority of its shares. Dell gained the stake through its acquisition of EMC, which was VMware’s previous majority owner. VMware envisioned independence as a strategic benefit, allowing it to forge new alliances with a variety of technology providers. It also believed that Wall Street would reward it with a higher share price if it separated from Dell.

Instead, the company’s shares declined 19 percent from the start of the year to Friday, the last trading day before Bloomberg reported on the negotiations with Broadcom.

Brad Zelnick, an analyst at Deutsche Bank, said that VMware has lost luster with public investors because it has struggled to compete with newer cloud technology.

“They’ve been challenged as a business in adapting to this transition,” Mr. Zelnick said.

That stock slump made VMware a more attractive target for Mr. Tan, and potentially other suitors. The terms of the deal with Broadcom include a “go-shop” period, which gives VMware’s management 40 days to seek a better offer from a different buyer. Acquiring VMware could make sense for several other technology companies, such as IBM or Intel.

If shareholders and regulators approve the deal, VMware’s long-desired independence will come to an end.