Still, interviews with four people briefed on the deal revealed that the Saudis had been discussing a possible partnership with a number of other firms as well, and formally decided on Blackstone — a fund-raising juggernaut that manages funds larger than the economies of some nations — only after Mr. Schwarzman had started advising the president.

In addition to Mr. Schwarzman’s prominence, the Saudi sovereign wealth fund was drawn to the firm’s record of generating huge investment returns and building new business lines, from real estate to hedge funds, according to the people with knowledge of the deal.

There is no suggestion that Blackstone did anything wrong. Instead, the company’s experience illustrates the incentives that corporate leaders have to develop strong ties with Mr. Trump — the country’s businessman in chief — and the reputational risks associated with those relationships when Mr. Trump veers off course, as he did this past week.

“Public service is a core value for people of my generation,” Mr. Schwarzman said in a statement. “It’s a great privilege to be asked to help the country — even if it occasionally comes with some degree of criticism.”

Mr. Trump’s visit to Saudi Arabia pushed the Blackstone deal forward so that it could be announced while the president was there, two people briefed on the agreement said. And the new fund, which plans to invest in projects like aging bridges and roads primarily in the United States, is expected to benefit from any federal infrastructure plan that may materialize under the Trump administration.

A Blackstone spokeswoman said that while a federal plan “would be helpful, our business is not at all dependent upon it since state and local governments — which build the vast majority of projects — are already pursuing billions of dollars in public-private partnerships.”

Some of the other investment firms that were in discussions about a Saudi partnership, including Brookfield and the Carlyle Group, had more experience in managing infrastructure funds and are still in talks with the Saudis according to the people who were not authorized to speak about a private deal.