Powys council employs about 8,000 people
Powys council and the county's local health board (LHB) have voted to join forces in one of the first mergers of its kind.
They said that by merging, which is planned for April 2012, they could improve the delivery of services.
The local authority and the LHB have accepted the proposal in principle subject to further discussions and a "positive response from the public".
They unveiled plans to develop closer working ties in April.
The plans were recommended for approval by the council, while the LHB met roughly at the same time at a separate meeting.
The votes in favour followed the publication of a report, commissioned by both and published in July, recommended merger.
It said Powys could be at the "front of groundbreaking improvements in public services".
It is believed to be one of the first mergers of its kind.
LHB chairman Chris Mann said: "Our priority is to deliver the best possible services to our people, and make the best possible use of their money.
"Working as a single organisation will help us deliver both of these benefits. That's why I think it's excellent news that the merger has been approved today.
"We face the same challenges, we serve the same people. That's why I think a single organisation is the right way forward for Powys."
Powys council's board chairman Michael Jones said there were already strong links between the two organisations, but they believed more could be achieved.
"The eventual merger of the two could trigger significant service improvements by developing a more integrated approach to our work," he added.
"Some changes will not be immediate or visible.
"But, we are confident that with goodwill and effort we can produce something to be proud of.
"It's a unique opportunity to do something special in Powys and improve the quality and efficiency of services for all."
Brecon and Radnorshire AM Kirsty Williams and her Liberal Democrat colleague in Montgomeryshire, Mick Bates, welcomed the merger.
Ms Williams said: "This is great news for the county and for its residents.
"It will allow them to shape Powys' health service to fit their own needs and wants rather than having policies imposed from the (Cardiff) Bay bubble."