At present some hospitals charge for wi-fi and others have no access at all.
The move is a recommendation from a government-commissioned report on improving the use of online technology in the health service.
The government has set no deadline for the plans but expects the NHS to be "digital and paperless" by 2020.
Money for the service is being provided from a Â£1bn technology fund.
Mr Hunt said: "Everyone using the NHS expects it to be a world leader in digital healthcare and free wi-fi is an essential part of making that a reality.
"It will give patients and staff the ability to access the services they need as well as freeing up clinical time and reducing overall costs."
In some hospitals paper charts have already been replaced by mobile clinical systems and tablets, allowing for data to be shared around the building.
The Department of Health said greater use of e-prescribing could reduce medication errors by 50%.
It also believes the plans will encourage the use of technologies that could help alert doctors and nurses to medical problems and reduce paperwork and errors.
Patients could also wear monitors to alert medical staff to issues, such as diabetics who have experienced "largely avoidable" hypoglycemic episodes while in hospital.
The Department of Health was unable to say what proportion of NHS facilities already provide free wi-fi.

King, known for his hits Lucille, Sweet Black Angel and Rock Me Baby, died in his sleep in Las Vegas.
Born in Mississippi, King began performing in the 1940s and was inducted into the Blues Foundation Hall of Fame and the Rock and Roll Hall of Fame.
He was recently taken to hospital with a diabetes-related illness.
Rolling Stone magazine once ranked BB King in third place in its list of the 100 greatest guitarists of all time, just below Jimi Hendrix and Duane Allman.
A former farmhand, King was awarded his 15th Grammy award in 2009 for his album One Kind Favor.
Even until recently, King performed in at least 100 concerts a year.
Free wi-fi is to be provided in all NHS buildings in a bid to improve services and reduce costs, Health Secretary Jeremy Hunt said.
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The 'King of the Blues' guitarist and singer, BB King, has died aged 89, his lawyer says.