WASHINGTON » As Medicare and Medicaid reach their 50th anniversary on Thursday, the two vast government programs that insure more than one-third of Americans are undergoing a transformation that none of their original architects foresaw: Private health insurance companies are playing a rapidly growing role in both.

More than 30 percent of the 55 million Medicare beneficiaries and well over half of the 66 million Medicaid beneficiaries are now in private health plans run by insurance companies like the UnitedHealth Group, Humana, Anthem and Centene. Enrollment has soared as the government, in an effort to control costs and improve care, pays private insurers to provide and coordinate medical services for more and more beneficiaries.

Although the programs remain highly popular with patients, skeptics question whether the use of private plans will save the government money in the long run and worry that the plans may skimp on care. But both programs served as foundations for the 2010 Affordable Care Act which, like the newer versions of Medicare and Medicaid, uses a combination of government money and private insurance to provide coverage.

This week the White House is using the half-century anniversary of Medicare and Medicaid to portray the Affordable Care Act as a logical extension of the two social insurance programs, which are part of the fabric of American life. Administration officials hope that President Barack Obama’s health care program will one day be as widely accepted as Medicare and Medicaid are now.

“The Affordable Care Act expanded Medicaid and built a model that helped fill some of the gaps between Medicare and Medicaid,” Jason Furman, chairman of the president’s Council of Economic Advisers, said in an interview Wednesday. “At the same time, it is rooted in the private sector and competition.”

When President Lyndon B. Johnson signed the bill creating Medicare and Medicaid on July 30, 1965, he made clear his ambitions for the programs: They would extend “the miracle of healing to the old and to the poor.” The legislation fulfilled decades of Democratic dreams, but, unlike the Affordable Care Act, it was passed with votes from a substantial number of Republicans.

The architects of Medicare and Medicaid, among them Wilbur J. Cohen and Robert M. Ball, had concluded that private insurance was out of reach for many older and low-income Americans, who could not obtain affordable coverage in the commercial market. At the time, Ball was the Social Security commissioner, and Cohen was a top official at the Department of Health, Education and Welfare, who later became secretary. Both men had been inspired by the New Deal and had worked for decades on Social Security.

“They believed that commercial health insurance had failed the elderly, and they wanted to replace it with social insurance, as a first step toward similar coverage for the rest of the population,” said Theodore R. Marmor, a Yale professor and historian of Medicare.

In a secretly recorded telephone conversation in March 1965, Cohen described the Medicare bill that had just been approved by the House Ways and Means Committee. “Quite frankly,” Cohen told Johnson, “there’s no longer any room for the private insurance companies to sell insurance policies for people over 65.”

The committee chairman, Rep. Wilbur D. Mills, chimed in, saying, “We have written the insurance people, I must admit, completely out” of the bill.

In the original versions of Medicare and Medicaid, beneficiaries could go to any doctor or hospital, and the government would pay providers a fee for each service. By contrast, in private managed-care plans, beneficiaries use a network of doctors and hospitals, and the federal or state government pays insurers, which receive a fixed amount per member per month.

The original setup of Medicare and Medicaid began to change in the early 1980s after Congress and the Reagan administration created incentives for private insurers to contract with Medicare. Enrollment rose and fell, as federal officials tinkered with reimbursement rates.

In the last decade, as private insurers stepped up their marketing of Medicare plans and baby boomers accustomed to managed care reached retirement age, enrollment in the private Medicare plans, called Medicare Advantage, surged. About 99 percent of beneficiaries now have the option to enroll in a Medicare Advantage plan, and the average beneficiary has a choice of more than a dozen plans.

In interviews, Medicare beneficiaries expressed a high degree of satisfaction with both the original government-run program and the private alternatives, which include health maintenance organizations and other forms of managed care.

“For seniors on fixed income, an HMO provides the best bang for the buck,” said Ann E. Mason, 74, of Rochester, New York.

Like many older Americans, she found that a Medicare Advantage plan offered better value than the combination of traditional Medicare and a supplementary insurance policy to fill gaps in Medicare, for expenses like co-payments and deductibles.

Ann C. Dorsey, 65, of Atlanta, qualified for Medicare several years ago after she developed a rare heart tumor and became disabled. She has invited insurance agents to her home to explain their plans and is pleased with her Cigna HMO.

“Anybody who doesn’t look at Medicare Advantage is nuts,” said Dorsey, who said she saved at least $1,000 a year, because of lower out-of-pocket expenses. But, she said, before selecting a plan, beneficiaries need to do their homework, comparing benefits, physician rosters and prescription drug lists of different plans.

Yet even with managed care, big questions remain about how to finance Medicare and Medicaid for the next 50 years.

In Congress and in state legislatures, which help pay for Medicaid, the costs continue to cause anxiety. Under the Affordable Care Act, more than half the states have expanded eligibility for Medicaid, and state officials have enrolled most new beneficiaries in private plans.

In many states that expanded Medicaid, enrollment has far surpassed expectations, evidently because state officials underestimated the demand for insurance and the proportion of eligible low-income people who would sign up.

Michigan, for example, has signed up 600,000 people in 16 months — more than it expected to enroll in five years. Nearly 80 percent of the new beneficiaries are in private managed-care plans.

Congress did reduce payments to private Medicare Advantage plans in the Affordable Care Act, to help offset the cost of the legislation, and insurers predicted that enrollment would decline. Instead, it has increased to 16.6 million people, from 11 million in 2010. The Congressional Budget Office predicts that the number will reach 30 million by 2025.

Experts say that private plans are not for everyone.

“Medicare Advantage plans are often more stingy with benefits,” said Judith A. Stein, who has represented hundreds of beneficiaries as executive director of the nonprofit Center for Medicare Advocacy. “We have seen many cases in which people who are really sick cannot get coverage for nursing or therapy at home or in a skilled nursing facility — coverage that they would be able to get if they were in traditional Medicare.”

For both Medicare and Medicaid, paying for the rising cost of prescription drugs remains a daunting challenge.

“Medicare Advantage provides great coverage,” said Nancy R. Corey, 68, a retired schoolteacher in Dayville, Connecticut. “But drug costs have skyrocketed. I’ve spent as much on my main medications in the first six months of this year as I did in all of 2014.”

Improper payments, including fraud, still bedevil Medicare and Medicaid, irking beneficiaries and politicians. The Government Accountability Office, an investigative arm of Congress, says that improper payments cost the federal government $60 billion in Medicare last year, or 10 percent of program spending, and $17.5 billion in Medicaid, or 6.7 percent.

Last month, the Justice Department, in a nationwide sweep, accused 243 people of Medicare fraud schemes involving more than $700 million in billings for services that were unnecessary or never provided. Among those charged were 46 doctors and other professionals who offered home health care, psychotherapy, physical therapy, diagnostic tests and prescription drugs.

With Medicaid rolls climbing to record levels, especially in states that expanded eligibility under the Affordable Care Act, Medicaid officials also face a huge challenge finding enough doctors. In many states, doctors have been reluctant to accept Medicaid patients, in part, they say, because the fees are low.

Elizabeth A. Persaud, 36, of Alpharetta, Georgia, who has a form of muscular dystrophy, receives home and community-based services through Medicaid. A personal attendant helps her get out of bed, shower, eat and go to work.

Medicaid is a boon that allows her to preserve her independence, Persaud said, but she added: “It is difficult to find doctors in my area who accept Medicaid. I often have to have someone drive me far away to see a specialist — a cardiologist, a neurologist, a dentist or an eye doctor.”

Sara Rosenbaum, a professor of health law and policy at George Washington University, said that Medicaid plans were “once the scourge of poor communities,” taking money without providing much care. But now, she said, they provide invaluable services to people with severe physical and mental health problems, as states often require those services in their contracts with insurers.

“The care is light-years better than what a Medicaid beneficiary would face if she had to go find an orthopedist, a rheumatologist or a podiatrist or get specialty drugs on her own,” Rosenbaum said.

Many Medicare patients agree.

In a comment echoed by other Medicare beneficiaries, Judith M. Anderson, 69, of Chicago said: “After a lifetime of an utterly boring personal health care history, I was diagnosed with cancer in 2013. Without Medicare, I would be bankrupt and probably dead by now. I had three surgeries and chemotherapy and paid less than $1,000 out of pocket. I love Medicare.”