Frimley Health NHS Foundation Trust has 285 full-time vacancies across three sites, which cover Surrey and Berkshire.
The high cost of living in the south of England is said to be a factor affecting recruitment.
Each successful applicant will receive a maximum of £1,340 in subsidies.
Nurses will be offered accommodation at Wexham Park Hospital in Slough, Frimley Park near Camberley and Heatherwood Hospital in Ascot.
Marko Novosil moved from Croatia to become a nurse at Wexham Park after hearing about the incentive.
"The crucial thing for coming here was the support. I realised that when I started I would get the free accommodation which helped me settle in", he said.
Wexham Park Hospital matron Helen Noakes said: "Rental prices are higher in this area, which means people do struggle and the one thing that we can offer people is the free accommodation when they start.
"Longer term we would look to help them find somewhere in the local area to live."
Currently the average monthly rent for a one-bedroom property in Slough is £897, whereas the average for the same sort of property in Camberley is £930.
The average cost for a room in both areas ranges from £500 to £550.
Nursing job applicants are being offered two months free accommodation in a bid to quell staff shortages at a hospital trust.