The deal - which could be worth $ 40 billion (£ 30.8 billion) - was reached by the company's current owner, Japanese tech conglomerate Softbank, four years after the company's acquisition.
ARM technology is at the heart of most smartphones among other devices.
Two of the company's co-founders had warned against the acquisition.
Hermann Hauser and Tudor Brown had suggested that the Cambridge-based designer should remain "neutral," rather than being owned by a company like Nvidia, which makes its own processors.
The concern is that there would be a conflict of interest as ARM's customers would become addicted to a business with which many also compete for sales.
Furthermore, the two co-founders also said that once ARM was owned by an American company, Washington could have attempted to prevent Chinese companies from using its know-how as part of a larger trade confrontation between countries. .
Others, including the British Labor Party, had also urged the government to intervene to safeguard British jobs.
Chip makers
ARM creates computer chip designs that others customize for their own purposes. It also develops instruction sets that define how the software controls processors.
It is headquartered in Cambridge, but also has offices around the world, including a joint venture in Shenzhen, China.
Hundreds of companies license its innovations including Apple, Samsung, Huawei and Qualcomm.
When Softbank acquired ARM, it promised to keep the company's UK headquarters and increase the number of local jobs, which it did.
California-based Nvidia overtook Intel to become the world's most valuable chip maker in July.
Until now, he has specialized in high-end graphics processing units (GPUs). These are commonly used by gamers to provide more detailed images, as well as by professionals for activities such as scientific research, machine learning, and cryptocurrency mining.
But Nvidia is also one of ARM's customers, which uses its designs to create its Tegra line of computer processing units (CPUs).
