Princess Margaret Hospital is planning to pay for 43 beds in nursing homes to cope with winter pressures.
Six new beds are also opening in the hospital itself.
It usually costs between £340 and £400 a week per resident in nursing homes.
Based on what Swindon Council pays for nursing home care for the elderly, this means the hospital could be facing a bill of at least £14,620 per week to ease its bed shortage.
The announcement comes a day after the Evening Advertiser revealed that some patients were sleeping on trolleys or mattresses on the floor, including our own reporter Shirley Mathias.
A new ward containing eight beds was opened earlier this week as part of the package of measures to relieve winter pressures.
Sonia Mills, chief executive of the Swindon and Marlborough NHS Trust, which runs the hospital, said 43 beds would be made available this winter in nursing homes. These are for people who are well enough to leave hospital but too ill to go home.
"We are short of beds but we are doing our best to combat this," said Ms Mills.
"It has been incredibly busy during the past few weeks. Winter has started very early. On Monday, for example, we took in 40 medical admissions when the normal admission rate for this time of year is 30.
"This is an increase of 33 per cent which is a significant jump. And we are not the only hospital affected."
She said in the next ten days 22 patients would be transferred to nursing homes, to clear beds for others. Another 21 nursing home places, paid for by the hospital, would be available in February when the pressures are usually really severe.
Over the past two weeks the Evening Advertiser has been publicising the hospital's campaign to get former nurses back to work.
There are currently 70 nursing vacancies within the trust and within the next few weeks more than 30 nurses from abroad will be arriving to work at PMH.
Ms Mills said: "We are taking more people on and as a result of this we will be able to open six more beds in the near future."
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