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.