Philip H. Knight, the co-founder and chairman of Nike Inc., said on Monday that he had pledged to give Stanford University $400 million to recruit graduate students around the globe to address society’s most intractable problems, including poverty and climate change.

The gift to the new Knight-Hennessy Scholars Program, which is modeled on the Rhodes scholarships, matches one of the largest individual donations ever to a university, the $400 million that John A. Paulson, the hedge fund tycoon, gave to Harvard last year to improve its engineering school. The Stanford project is meant to improve the world.

“This is using education to benefit mankind and I think it really could be transformative,” Mr. Knight said in a phone interview. “I jumped on it right away.”

Its ambitious mandate is the brainchild of Stanford’s president, John L. Hennessy, a computer scientist and tech entrepreneur, who plans to step down this summer. During his 16-year tenure, Mr. Hennessy nurtured the school’s symbiotic relationship with Silicon Valley and increased Stanford’s endowment to more than $22 billion from about $9 billion in 2000.

The program, which will be announced on Wednesday at Stanford, has raised $750 million, making it one of the largest fully funded scholarship endowments in the world.

These kinds of megagifts to elite universities have their critics, who argue they are more about prestige and ego than academic excellence. “This is just part of the crazy arms race between the top schools with no connection to reality,” said Malcolm Gladwell, a writer for The New Yorker and the author of “The Tipping Point” who posted scathing Twitter messages last year about Mr. Paulson’s gift to Harvard. “If Stanford cut its endowment in half and gave it to other worthy institutions,” he said, “then the world really would be a better place.”

According to the Council for Aid to Education, less than 1 percent of the nation’s colleges received 28.7 percent of all gifts in 2015.

The former Secretary of State Condoleezza Rice, who is now a professor at Stanford, called it “an exciting place at the heart of Silicon Valley.”

She added, “It’s a place where people are innovating all the time and it can attract the best people from all over the world.”

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.

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?’ ”

A representative for Mr. Zuckerberg pointed out in response that, among other things, graduation rates in Newark had gone up 13 points in the last few years.