Wolverhampton's New Cross Hospital will have to find £5.5m of its £21m debt by 2012 - the rest will be paid off by other authorities.
The £50m deficit owed by University Hospital of Coventry and Warwickshire will also be paid off.
Health chiefs said the agreement came after months of talks.
The debt owed by Coventry's hospital will be paid off by the West Midlands Strategic Health Authority, the Warwickshire Primary Care Trust (PCT) and by the sale of hospital land.
The trust that runs the Wolverhampton hospital will use £3.2 million it received from the sale of the city's old eye infirmary.
An extra £6.1 million will come from the regional strategic health authority and £6.2 million from the city's PCT.
Martin Lee, chief executive at University Hospitals Coventry and Warwickshire NHS Trust, said the news gave them a "firm financial footing and renewed optimism."
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