International students are a boon for American universities. (Michael Okoniewski/Bloomberg News)

Foreign countries are sending tens of thousands of students to American universities every year, propping up school budgets and contributing billions of dollars to the U.S. economy. 

And no city sends students to American universities quite like Seoul. The South Korean capital funneled more than 56,000 students into U.S. bachelors, masters, and PhD programs between 2008 and 2012, according to a new study by The Brookings Institute. Beijing, China, the second biggest contributor, sent almost 50,000 students over that period; Shanghai, China, the third biggest contributor, send just under 30,000 students; and Hyderabad, India, the fourth largest, send just over 26,000.

In all, more than 1.1 million students flocked to the United States between 2008 and 2012. Last year alone, more than 800,000 international students came to the country to pursue higher education. Today, America's colleges and universities host nearly a quarter of all students studying abroad worldwide. And it isn't merely big name universities and Ivy League schools that are reeling them in—state universities and smaller metropolitan cities are seeing their foreign student bodies increase, too.

"They have been really big boosts to big state universities that have seen their budgets cut in recent years," said Neil Ruiz, a senior policy analyst at The Brookings Institute, who authored the study.

International students also contribute many billions of dollars a year to the U.S. economy. By Brooking's estimates, foreign students payed almost $22 billion in tuition and another $13 billion in living expenses between 2008 and 2013 (which was more than welcome, considering how poorly college endowments performed during the recession).

"Universities and entire metropolitan areas, really, are realizing that in the short term they bring a lot of money into the economy," Ruiz said.

Seoul is particularly fruitful in that regard—the students it sends to the U.S. aren't merely numerous, they're also willing spenders. No city dished out more in educational spending between 2008 and 2012 than students from South Korea's capital city. Foreign students from Seoul spent well over $1.3 billion over that period. Those from Beijing spent just under $1.3 billion; those from Shanghai spent a tad less than $800 million; and those from Mumbai, India, spent just over $400 million.

The U.S. higher education system is becoming more and more dependent on foreign students to help foot their bills each year. "The percentage of students in the U.S. has remained constant at just above 3 percent," Ruiz said. "But the percentage of spending has increased."

That's because foreign students tend to pay full tuition, especially when enrolling in bachelor's programs, since they are not eligible for many financial aid programs. "Some PhD programs wouldn’t even exist if it wasn’t for foreign students," Ruiz said. Purdue's graduate engineering program is perhaps one of them—the majority of its students now come from overseas.

But foreign students aren't merely coming for college or other graduate degrees, and then leaving. Almost 50 percent of them now stick around for an extra year after school, the study notes.

What that suggests is a desire among those earning degrees in the country to stay and work for extended periods of times. Considering that more than two-thirds of foreign students are studying science, technology, engineering, and math, or business and marketing—degrees that are especially attractive to employers—compared to fewer than 50 percent of domestic students—it might also be to the benefit of local metropolitan economies, at least in the short term.