Baton Rouge-based home nursing firm Amedisys Inc. will buy Associated Home Care, a Boston-area private-duty home health agency, for $28 million under a deal announced Thursday.

Typically, private-duty nursing firms’ services don’t accept Medicare. In the third quarter, 75 percent of Amedisys’ home nursing revenue came from Medicare and 94 percent of hospice revenue.

Associated Home Care is Amedisys’ first acquisition of a private-duty company and an important step toward Amedisys’ long-term strategy, said President and Chief Executive Officer Paul Kusserow. Private-duty services complement Amedisys’ home nursing and hospice businesses and will improve patients’ continuity of care, he said.

Andover, Massachusetts-based Associated Home has 1,500 employees and provides care for 5,000 seniors each day. In addition to its headquarters, the company has nine branch locations in Massachusetts. Associated Home generates about $40 million a year in revenue.