The Biden administration, in one of its last major policy directives, will propose that Medicare and Medicaid cover obesity medications, a costly and probably popular move that the Trump administration would need to endorse to become official.

The proposal would extend access of the drugs to millions of Americans who aren’t covered now.

The new obesity drugs, including Wegovy from Novo Nordisk and Zepbound from Eli Lilly, have been shown to improve health in numerous ways, but legislation passed 20 years ago prevents Medicare from covering drugs for “weight loss.”

The new proposal sidesteps that restriction, specifying that the drugs would be covered to treat the disease of obesity and prevent its related conditions.

“We don’t want to see people having to wait until they have these additional diseases before they get treatment,” said Chiquita Brooks-LaSure, the administrator of the Centers for Medicare and Medicaid Services, or C.M.S., noting the growing medical consensus that obesity is a chronic health condition.

The classification would also mean that every state Medicaid program would be required to cover the drugs starting in 2026. Currently, only a handful do.

C.M.S. estimates that around 3.4 million more patients in Medicare would become eligible for obesity drugs, and around four million patients in Medicaid would gain coverage, costing the programs billions of dollars. Medicare covers Americans 65 and older; Medicaid covers poor and disabled Americans.