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Charles said he was "enormously touched" to be asked to open the temporary facility at the ExCel center in east London and paid tribute to everyone, including military personnel, involved in its "spectacular and almost unbelievable" nine-day construction.
"An example, if ever one was needed, of how the impossible could be made possible and how we can achieve the unthinkable through human will and ingenuity," he said via video link from his Scottish home of Birkhall.
"To convert one of the largest national conference centres into a field hospital, starting with 500 beds with a potential of 4,000, is quite frankly incredible."
The new National Health Service hospital will only care for people with COVID-19, and patients will only be assigned there after their local London hospital has reached capacity.
Charles, who earlier this week emerged from self-isolation after testing positive for COVID-19, said he was one of "the lucky ones" who only had mild symptoms, but "for some it will be a much harder journey."
He expressed his hope that the hospital "is needed for as short a time and for as few people as possible."
The hospital is named after Florence Nightingale, who is widely considered to be the founder of modern nursing. She was in charge of nursing British and allied soldiers in Turkey during the Crimean War of the 1850s, her selfless care earning her the reputation as the "Lady with the Lamp."
Natalie Grey, the head of nursing at NHS Nightingale, unveiled the plaque formally opening the hospital on the prince's behalf.
Further new hospitals are being planned across the U.K., including in Birmingham, Glasgow and Manchester, to alleviate the pressure on the NHS during the coronavirus pandemic.
"In these troubled times with this invisible killer stalking the whole world, the fact in this country we have the NHS is even more valuable that before," said Health Secretary Matt Hancock, who also contracted COVID-19 and only emerged from his self-isolation on Thursday.
The number of people in Britain dying after testing positive for COVID-19 has been increasing sharply over the past couple of weeks. The latest U.K. figures showed that the number of people to have died increased in a day by 569 to 2,921.
Like many other countries, Britain is in effective lockdown, with bars and nonessential shops closed in order to reduce the rate of transmission, the hope being that it will eventually reduce the peak in deaths. Hancock would not be drawn across several interviews about when he expects the peak to be, beyond that it's likely to occur in "coming weeks."