The Health and Human Services Department yesterday approved final regulations to allow Medicaid to pay for home-care services for poor people who otherwise would have to be in a nursing home or hospital.

HHS Secretary Margaret M. Heckler said in a statement that she had signed final regulations authorizing states to receive waivers enabling them to pay for the home services, which include hospice care and homemaker services.

Interim regulations have been in effect since 1981, and Heckler said HHS has granted 86 waivers in 46 states for such care. Another 25 waiver requests are pending, she said.

The regulations allow Medicaid to grant home care in some fields where it is cheaper to look after a person at home than in an institution. The regulations specify that such care can be provided in the homes at Medicaid expense only if it is cheaper than institutionalization and only if the patient would have to be institutionalized were home services not provided.

The rules originally were prompted by the case of Katie Beckett of Cedar Rapids, Iowa, whose parents complained to their representative that Medicaid regulations forced them to seek hospital treatment when their daughter's viral encephalitis could have been treated more cheaply at home. President Reagan cited the case at a November 1981 news conference as an example of "hidebound regulations."