It will mean patients can use their smart phones or other devices to go online to keep in touch with friends and family while they are in either the Royal Shrewsbury Hospital or Telford's Princess Royal Hospital.
It comes after officials from Telford and Wrekin Clinical Commissioning Group offered to provide £200,000 in match funding to support the Shrewsbury and Telford Hospital NHS Trust-led project.
Simon Wright, chief executive of SaTH, said: "We are constantly looking at ways to improve the experience of our patients, visitors and staff.
"Any length of stay in hospital, whether you are the one receiving treatment or supporting a loved one, can be, at times, frustrating or boring.
"While we already provide free patient wi-fi in a number of areas where we know patients are likely to have a lengthy stay – such as our chemotherapy day centre and the women and children's centre – we have been keen for some time to expand this to cover all of our hospital sites.
"We are delighted our CCG partners have offered to match our funding for this important scheme.
"But this will not just benefit our patients and visitors. Technology is playing an increasing role in almost everything we do and being able to access wi-fi across our sites will help all of our staff manage the increasing demand on their time as well as improving the accuracy of record keeping and improving patient safety."
David Evans, chief officer for Telford and Wrekin CCG, said: "NHS commissioners are delighted to be able to fund this initiative.
"Free wi-fi throughout the trust's facilities has obvious benefits for patients that can help improve their experience in hospital.
"However there are also very clear benefits for clinicians too.
"It will allow access to a range of apps which put huge amounts of information at their fingertips and will also make it easier to be in contact with colleagues wherever they happen to be."
In December Health Secretary Jeremy Hunt announced that free wi-fi would be provided in all NHS buildings in England in a bid to improve services and reduce costs.
The Government has set no deadline for the plans but expects the NHS to be "digital and paperless" by 2020.