Beyond what Mr. Trump and Mr. Son said, “we aren’t able to say more,” a SoftBank spokesman in Tokyo, Matthew Nicholson, said.

“I just came to celebrate his new job,” Mr. Son, 59, told reporters at Trump Tower. “I said: ‘This is great. The U.S. will become great again.’ ”

Such bold talk is customary from the American-educated Mr. Son, who has built one of Japan’s biggest personal fortunes through sometimes brash deal-making. SoftBank, which began life as a software distributor, became one of Japan’s biggest phone service companies through shrewd negotiations that gave the company early exclusive rights to the iPhone. It has since become a global empire with stakes in the likes of Sprint and Alibaba Group of China and in a welter of start-ups in the United States and abroad.

This year, Mr. Son struck a $32 billion takeover of ARM Holdings, a British chip designer whose products sit at the heart of devices like the iPhone.

Like the president-elect, Mr. Son has been known for sometimes impolitic remarks. As Mr. Son sought to compete against Verizon and AT&T with his investment in Sprint, he compared the quality of American wireless service to the air quality of Beijing. And he threatened to set himself on fire in the offices of Japan’s telecommunications regulator on at least one occasion.

In speaking with reporters alongside Mr. Trump on Tuesday, Mr. Son clutched what appeared to be a presentation from the meeting. One page featured the logos of both SoftBank and Foxconn, the Taiwanese manufacturing giant that assembles Apple’s iPhone. On the page — and circled — was the text committing to investing $50 billion in the United States and generating 50,000 jobs over the next four years.

Below it appeared to be Mr. Son’s signature.

Foxconn said in a statement that it was in preliminary discussions about a potential American expansion, adding that the scale had not yet been decided. Foxconn has said in the past that it plans to expand its limited operations in the United States.