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 Obama’s health care program will one day be as widely accepted as Medicare and Medicaid are now.