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Along the upward journey to middle-class status, a growing number of people around the world are working up a voracious appetite for all-American exports including Footlongs, Big Macs and Extra Crispy Chicken Tenders.

Despite early signs that a fast-food diet is no healthier in Beijing than it is in Boston, consumers new to middle-class dining seem less concerned about the health risks of the high-fat, high-sodium fare that many Americans now seek to avoid.

As the U.S. economy slogs along at a tepid pace, household incomes in much of the developing world are leaping ahead. Over the next two decades, those gains are expected to introduce billions of new consumers to menus from fast-food chains that are among some of the most iconic American brands.

And as many chains have saturated the U.S. market (and American tastes have shifted) the fast-food industry is finding a hungry market in far-flung locations, from Malawi to Mongolia.

"A lot of domestic chains are completely refocusing their business on the international market," said IBISWorld Industry analyst Andy Brennan. "And most of them have been quite successful at it."

IBISWorld pegs global fast-food sales at $190 billion but does not break out non-U.S. sales.

That is because for most fast-food chains, the formula that worked at home—low-cost menu items, prepared consistently and served quickly—seems to translate well for foreign consumers with newfound disposable income.

(Read more: A new species? The elusive nature of the global middle class)

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These companies are also riding a wave of global brand awareness, thanks to increased international travel and the powerful reach of the Web.

For many new arrivals to middle-class life, a meal at an iconic American fast-food outlet also bestows a level of prestige, according to Brennan.

"It's a real status symbol to be eating in an American restaurant in Asia," he said.

Yum Brands—the parent company of KFC, Pizza Hut and Taco Bell—generated more than 70 percent of its profits, or $1.1 billion, outside the U.S. last year, up from just 20 percent 15 years earlier.

(Read more: Higher bills? Thank for emerging middle class)

"We believe we have a long runway for growth in emerging markets like China, India, Africa, Russia, Indonesia, Vietnam and many others," a Yum spokeswoman said in email.

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That overseas growth comes as the company has an increasingly tough time finding a U.S. location that isn't already well-supplied with Hot Wings, Cantina Double Steak Quesadillas and Ultimate Cheese Lover's Pizza. In the top 10 emerging markets, Yum Brands has just two stores per million people—compared with 58 stores per million in the U.S.

As any traveler to a foreign country will tell you, adapting to strange tastes and diets can be challenging.

More than half of Subway's new stores last year were opened outside the U.S. by franchisees and other business partners. When it began expanding globally more than a decade ago, some of those partners "took local tastes a little too far," according to Don Fertman, Subway's chief development officer.

Japan franchisees tried to downsize the company's flagship Footlong sandwich on the theory that local customers weren't interested in larger portions.

"That's what Subway is known for," said Fertman. "So that didn't really work out."

(Read more: Singles Day supercharges China's new middle-class consumers)

Appealing to local markets also involves adapting a store's physical design and layout to conform to local tastes in decor and architecture—a move that can also backfire. Fertman said an Austrian partner once tried to introduce a "modern, cold look that was virtually unrecognizable to Subway customers."

Fast food has found a welcome market abroad, as a growing middle class hungers for the greasy, quick fare. Eugene Hoshiko / AP

"It was more like a disco," he said. "All steel and rock. So folks that were looking for Subway weren't finding it."

But adhering strictly to the original formula isn't always possible, no matter how successful it is with American consumers.

McDonald's offers customers in India a potato-based veggie burger, McAloo Tikki or the McCurry, served with or without chicken. It includes curried broccoli, baby corn, mushrooms and red bell pepper, with creamy sauce on a baked crust. In many Latin American countries you'll find the McMollette—an English muffin served with refried beans, cheese and salsa.

In Saudi Arabia, Subway's menu sticks with Halal foods and preparation methods. And if you're looking for a Subway sandwich in any other predominantly Muslim or Hindu country, don't bother asking for sliced roast beef or ham. Instead, there's a choice of turkey or lamb cold cuts on your Footlong.

Finding those ingredients—especially in parts of the world with limited infrastructure and poorly developed distribution systems—poses a major challenge.

"Even the mature companies can have supply chain issues overseas," said IBISWorld's Brennan. "That's really an unpredictable factor."

Yum Brands felt the full effect of those risks in December, when Chinese food safety agencies launched a probe of the company's supply chain after excess levels of antibiotics were found in chicken from two suppliers. Yum was not fined, but the probe sparked a widespread backlash in Chinese media and on social media sites.

In April, reports about a new bird flu renewed local concerns about the safety of its chicken. Sales plummeted at its KFC outlets, though the company says they have since begun to recover.

American fast-food chains have also been wrestling with a wider range of health concerns at home, as many consumers are changing domestic eating habits in response to an ongoing obesity epidemic. Many diners are now paying more attention to the long-term health impact of the high-fat, high-sodium fare that has been long been a best-selling fast-food industry staple.

So far, those concerns have had much less impact on sales in emerging markets, where entrance to the middle class includes consumption of higher-calorie, higher-fat food products that are only available with more disposable income.

That may another reason America's food makers are finding a more welcoming clientele in the developing world.

"Obesity is a sign of wealth," said Brennan. "The prestige factor of these fast-food menus overrides the health concern to a degree."

—By CNBC's John W. Schoen. Follow him on Twitter @johhwschoen.

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