CHATTANOOGA, Tenn.—The Obama administration and governors from Michigan to North Carolina have a solution for some of the U.S. manufacturing sector’s woes: German-style apprenticeship programs.

But their success is proving to be unusually one-sided, mostly drawing firms based in Germany and other non-U.S. countries. In North Carolina, “Apprenticeship 2000,” a program combining classroom work and on-the-job training, has drawn numerous German companies but so far only two U.S. firms, Ameritech Die & Mold Inc. and Timken Co.

In Michigan, where Republican Gov. Rick Snyder promised last year to “Americanize” the German model in his state, almost three-fourths of the participants are firms based overseas, mostly in Germany.

Both the White House and governors are trying to fight a so-called skills gap among U.S. workers that many businesses blame for the slow labor-market recovery. Although plenty of Americans are looking for work, employers often lament a lack of qualified workers—particularly young people.

Germany, in contrast, has a long record of finding a stronger fit between employees’ skills and employers’ demands. The success is reflected in a youth unemployment below 8%, the lowest of any advanced country and about half of the U.S. level. The apprenticeship system is credited as a leading driver of what many European economists call the German labor-market “miracle.”

“Vocational training is a well-recognized career in Germany that offers good income opportunities, whereas in the U.S. it is often associated with people who did poor at high school,” said Robert Lerman, an American University economics professor who studies apprenticeships.

Unlike in the U.S., where workers are largely hired and then trained for a company’s particular needs, German vocational training normally takes three years and is supposed to give apprentices a broader qualification beyond a single employer’s needs.

Amy Mitchum, center, left her job as a membership manager for a real-estate agency three years ago to join an apprenticeship program run by Volkswagen. Volkswagen Chattanooga

The students, paid by the companies, spend three to four days a week doing on-the-job training within companies and the rest of the time taking classes at public vocational schools. Curricula are developed by employers’ associations, trade unions and the federal government. Costs vary but average roughly $20,000 a year, typically for three years.

“The apprenticeship has been the best choice of my professional life,” said Amy Mitchum, a 37-year-old Tennessee resident who left her job as a membership manager for a real-estate agency three years ago to join an apprenticeship program run by Volkswagen AG. The German car maker’s Automation Mechatronics program gave her what is viewed globally as the gold standard for apprenticeships: a German vocational-training certificate.

She now earns $22 an hour, about 50% more than the median wage in her state. In a few years, she’ll likely move up to $30 an hour—alongside benefits including health insurance, a bonus, pension plan and good deals on cars. “I don’t see any reason why I might quit this,” she said. Now her husband works for Volkswagen, too.

Most U.S. workers avoid the same path for a number of reasons, experts say. Parents and educators tend to generally encourage young Americans to attend college. While businesses have an incentive to hire qualified workers, many resist investing in people who might leave. And the community colleges that are often at the center of apprenticeship programs tend to focus on local interests.

President Barack Obama, who has discussed the German model a number of times, has taken some action. The administration wants to double the number of apprentices within the next five years and plans to launch a $100 million program to expand apprenticeships.

Its success remains uncertain because of the U.S. educational system’s decentralized structure. While Germany has national standards for vocational training, it’s difficult for federal officials and state governors to set standards for community colleges.

“The power both of the federal and the state governments to push the collaboration between business and colleges on a regional level is limited,” said Monika Aring, an adviser to companies who has studied the issue for the International Labor Organization. Also, U.S. companies “are not used to collaborating with each other.”

Some corporate executives fear spending money on training could be a bad investment. Christian Koestler, vice president of operations at German manufacturer Stihl Inc. in Virginia Beach, Va., recently presented his vocational-training program to about 20 companies to seek their cooperation.

His American counterparts often asked him, “What if I invest in the people and then they leave?”

His reply: “It would be worse if you didn’t invest and they stayed their whole professional lives with you,” Mr. Koestler said. Only one company—based in Germany—joined the Stihl apprenticeship program.

At first glance, the fear of misinvestment seems justified. Studies show Americans between the ages of 16 and 25 change their jobs almost eight times, three times as much as Germans in the same age group. But the figures also could prove why the German model works: If companies invest in their workforce, the workers are much more loyal.

That’s why Mike Gidley, executive vice president of Pontiac Coil Inc., based near Detroit, thinks a German-style system benefits everyone. “It gives both our apprentices and us a huge competitive advantage,” he said. Mr. Gidley is the new chairman of the steering committee of MAT2, the vocational-training system introduced in Michigan. Under the program, firms must invest about $20,000 per person a year, but the apprentice must stay with the employer for at least two more years after the training.

“We have been struggling so long to find the technicians we need,” Mr. Gidley said. “The program is exactly what we needed.”

Corrections & Amplifications

“Apprenticeship 2000” is a technical-training program in North Carolina. An earlier version of this article incorrectly said the program is in South Carolina.

Write to Sven Böll at sven.boll@wsj.com