Older adults will be eligible for a second Covid-19 booster shot under a decision by federal health regulators, who are expected to authorize the additional shots for the broader population in the fall.

The Food and Drug Administration said Tuesday it had cleared extra shots of Pfizer Inc. and its partner BioNTech SE and from Moderna Inc. for adults 50 years and older.

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Under the authorization, the older adults can get the shots at least four months after a first booster dose. People will be able to choose between the two vaccines regardless of whether they earlier received a shot from Moderna or Pfizer.

In addition, the FDA cleared a second Pfizer-BioNTech booster dose for people 12 years old and up with weakened immune systems and who have received a first booster dose of any authorized Covid-19 vaccine. And the FDA also authorized a second Moderna booster for immunocompromised people 18 years old and above.

The extra doses will be available for use at physician offices, retail pharmacies, nursing homes and other vaccination sites once the Centers for Disease Control and Prevention signs off, which is expected to be soon.

The federal government has said it expects to have enough available supplies.

“Current evidence suggests some waning of protection over time against serious outcomes from Covid-19 in older and immunocompromised individuals,” said Peter Marks, who directs the FDA’s vaccines division. A second booster “could help increase protection levels for these higher-risk individuals,” he said.

Still, health authorities likely face an uphill battle in another vaccine campaign, with many in the U.S. already fatigued from vaccinations. About two-thirds of adults over 65 years old so far have received a booster, and less than half of the adult population has.

Some 23% of people who received at least one Covid-19 vaccine dose said they definitely won’t get a booster, according to a recent survey by the Kaiser Family Foundation, while 24% said they would only if they were required to do so. The rest said they would get one or would wait and see if they would get one.

The federal government has been providing vaccines free of charge in the U.S. under a program through which Medicare, Medicaid and private health insurers pay doctors, pharmacies and other vaccination sites for administering the shots. The uninsured could face fees for getting a shot, however, because a separate program covering the cost is winding down due to a lack of funding.

The thumbs-up for the fourth doses of the messenger RNA vaccines comes as Covid-19 cases and hospitalizations continue to fall but public-health experts express concerns about future surges, perhaps due to an Omicron sub-variant that is affecting parts of Europe.

The CDC already recommends four mRNA vaccine doses for certain people with weakened immune systems, such as transplant recipients and HIV patients. For those people, the extra dose is considered a booster shot after a three-dose primary series.

The second booster of the Pfizer-BioNTech vaccine would use the same, 30 microgram dose as the first three administered. The Moderna second booster is the same 50-microgram dose as the first booster, and half the dosage of each of the two shots in the primary vaccination series.

“Now, healthcare providers have the opportunity to advise higher-risk people about when and how to get boosted and build immunity in advance of future outbreaks,” said Moderna Chief Executive Stéphane Bancel.

More than 96 million people in the U.S. have received initial booster doses since they were first authorized for adults in November and then for adolescents at least 12 years old since January. The U.K., France, Germany and other countries have begun giving second booster doses to certain adults.

Boosters can bolster immune defenses against the coronavirus that fade over time, according to many health officials and vaccine experts. Researchers are divided, however, on the need to give a second booster, and when and who should be first to receive them.

People waiting to receive a booster shot at a Pfizer-BioNTech vaccination clinic in Southfield, Mich., in September.

Photo: Emily Elconin/Reuters

Research has shown that protection from shots falls after several months. Studies also have shown that an additional dose can boost immune systems that have weakened months after initial vaccination, and is more likely to neutralize the Omicron variant than two doses.

Yet there is limited and somewhat mixed data showing how well a fourth dose works.

Researchers who studied the efficacy of fourth doses of mRNA vaccines in healthcare workers wrote in the New England Journal of Medicine that the additional dose “may have only marginal benefits,” although they didn’t study older and vulnerable people.

In seeking authorization earlier this month, Pfizer cited two real-world studies from Israel that showed a second booster dose increased people’s antibody levels and lowered the rates of infections and severe disease.

Moderna said its request was based on recently published data from Israel and the U.S.

More definitive data is expected in the coming months. As part of a clinical trial looking at a vaccine tailored to target Omicron, Pfizer is evaluating how much protection a fourth dose of its current vaccine might provide. Pfizer has said it expects results during the first half of this year.

Moderna is testing fourth doses of its original vaccine in a mid-stage clinical trial, as well as booster shots that specifically target Omicron.

Given the limited data, the CDC isn’t expected to issue a strong recommendation urging those eligible to get a second booster. Rather, the agency is expected to simply advise that people who want to get a booster can go ahead.

The Biden administration has eyed broadening access to second boosters in the fall, when many people get their annual flu shots and might be inclined to get the extra Covid-19 dose at the same time.

Some researchers say a total of two or three shots are enough for most people for now, pointing to studies that found the regimens are keeping people from becoming hospitalized and dying.

Even those researchers say people with weaker immune systems, like the elderly and people at high risk for severe disease, may benefit from a second booster.

The Pfizer-BioNTech and Moderna vaccines are given initially as two doses, taken a few weeks apart. The CDC recommends third doses of the Pfizer-BioNTech and Moderna at least five months after the second dose.

—Betsy McKay and Peter Loftus contributed to this article.

Write to Jared S. Hopkins at jared.hopkins@wsj.com and Stephanie Armour at stephanie.armour@wsj.com