It will take on refurbishment work at the Russells Hall, Guest and Corbett hospitals and close down a fourth in Wordsley.
The consortium, which is called Summit Healthcare, will be responsible for the provision of non-clinical support services during and after the construction phase.
The total length of the contract is 40 years.
About 900 NHS staff are to be transferred to Interserve in two phases; the first will be this month.