Mr. Knight, a graduate of Stanford’s business school, gave that institution $105 million in 2006. Over the past 20 years, he has donated hundreds of millions to the University of Oregon, where he received his undergraduate degree.

Not every gift pledged by Mr. Knight has gone smoothly. In 2000, he withdrew a $30 million pledge to expand the University of Oregon’s football stadium after the school allied itself with a labor group that was critical of Nike factories overseas. The university president later reversed the decision and Mr. Knight restored the gift.

Image Stanford’s president, John L. Hennessy. Credit Steve Jennings/Getty Images

Mr. Knight is not the first billionaire to sponsor an international scholarship program. In 2000, Bill Gates, a co-founder of Microsoft, established the Gates Cambridge Scholarship for students of all nationalities to study at Cambridge University. In January, Stephen A. Schwarzman, the co-founder and chairman of the Blackstone Group, announced the first class of recipients of the Schwarzman scholarship, another Rhodes-like master’s program, at Tsinghua University in Beijing.

The Knight-Hennessy scholarship is not unique, but Mr. Knight may well be the rare billionaire benefactor who is willing to share top billing. “I think locking my name in with his for decades to come is an honor,” Mr. Knight said.

Mr. Hennessy described the fellowships as his legacy. “A few years ago I started to think about the one thing I could do at Stanford that could make a difference for the world in a bigger setting,” he said in a phone interview. “We could bring the best students from around the world to Stanford and produce a string of leaders educated in making positive change.”

Starting in 2018, the program will annually offer full tuition and board to 100 students — a third of them from the United States and two-thirds from abroad — who will gain admittance to one of Stanford’s seven graduate schools and commit to working on important issues in small, multidisciplinary teams.

One problem Mr. Hennessy said he might assign to a team is to analyze the $100 million donation that Mark Zuckerberg, the chief executive of Facebook, made to Newark public schools in 2010, and that has not been widely seen as a success. “Nobody understood the real difficulty in making significant change in the public education system,” Mr. Hennessy said. His scholars would be asked, he added, “ ‘How do you build a structure that will successfully deploy those funds for the benefit of all?’ ”