Patients will be able to look at their records, order repeat prescriptions and access 111 online for urgent medical queries.
The app will also allow patients to address longer-term concerns such as setting out their end of life care and organ donation preferences.
Hunt said: “The NHS app is a world-first which will put patients firmly in the driving seat and revolutionise the way we access health services.
“I want this innovation to mark the death knell of the 8am scramble for GP appointments that infuriates so many patients.
“Technology has transformed everyday life when it comes to banking, travel and shopping.
“Health matters much more to all of us, and the prize of that same digital revolution in healthcare isn’t just convenience but lives improved, extended and saved.”
Testing of the app, which will be available for patients in England, begins in September and it is expected to be ready to download from the App Store or Google Play in December.
Sarah Wilkinson, chief executive of NHS Digital, said: “We are working hard to deliver the Secretary of State’s vision for an NHS App which provides much easier access for individuals to key NHS services.
“We all know that demand for precious NHS services is escalating, and for a large portion of the population digital channels are a preferred means of access to data and services, so this is an opportunity to provide the easier access people want and relieve some burden from front-line providers.”
It comes as the NHS marks its 70th anniversary this week.
Matthew Swindells, NHS England national director of operations and information, said the app would allow patients to take charge of their own healthcare.
He added: “The new app will put the NHS into the pocket of everyone in England, but it is just one step on the journey, we are also developing an NHS Apps Library and putting free NHS Wi-Fi in GP surgeries and hospitals.”