In a statement on Thursday, the company said it had agreed to buy the software company in a transaction valued at $61 billion. The deal would give Broadcom popular computing tools used by a large swath of corporations.

The chip company said in a statement that it will pay $138 per share for the company. Before rumors of a deal began to circulate over the weekend, the stock price of VMware was more than 40 percent higher.

The combination of the two companies would make them a significant player. It would be the second-biggest proposed acquisition this year. Microsoft's $75 billion bid is the biggest. More than half a million customers of VMware are around the world, and the company counts all major cloud providers as partners. The chief executive of the company is Hock E. Tan.

Mr. Tan had been one of the most acquisitive forces in the chip industry, stitching together one deal at a time, until President Donald J. Trump blocked the proposed $117 billion takeover of the chip maker. The company moved its headquarters to San Jose, Calif., from Singapore.

Mr. Tan has changed his targets. He bought the software company CA Technologies for $18.9 billion and the 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, it would be Broadcom's flagship asset. In its last fiscal year, the company reported revenue of $12.9 billion. That was an increase from the previous year. The growth rate of the cloud-computing arms of Amazon, Microsoft and Google was much slower. Before the cloud boom, VMware depended on clients that still operate their own data centers.

A deal would be the latest in a series of changes. Pat Gelsinger, the company's long-time chief executive, left in January 2021. On May 12 it gained a new chief executive, Raghu Raghuram, and lost a chief operating officer, Sanjay Poonen. When it was spun off from Dell Technologies, the software maker became independent.

Mr. Gelsinger wanted to get rid of the personal computer maker that owned a majority of its shares. The previous majority owner of the company was Dell. It was thought that independence would allow it to forge new alliances with a variety of technology providers. If it separated from Dell, Wall Street would reward it with a higher share price.

The company's shares fell 19 percent from the start of the year to Friday, the last trading day before the negotiations with Broadcom were reported.

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

They have been challenged as a business in adapting to this transition.

The stock slump made it more attractive for Mr. Tan to look at VMware. The terms of the deal give the management of the company 40 days to find a better offer. It makes sense for IBM or Intel to acquire VMware.

If the deal is approved by shareholders and regulators, the independence of the company will come to an end.