The 99-year-old was guest of honour at the opening ceremony this afternoon, and appeared by video link in front of around 100 people.
The audience at the Harrogate Convention Centre gave Captain Tom, who will turn 100 later this month, a standing ovation as they wished him a happy birthday.
Captain Tom declared the new facility open following his £27 million fundraising effort during the coronavirus pandemic. Sitting with his daughter, Hannah Ingram-Moore, at his home in Bedfordshire, he said: "I'm absolutely in awe of what has happened.
"If you think all the kindness of the people in this country and throughout the world, who have given so much money to the fund to help our National Health Service, which you have got to agree is one of the best services that there is in the world."
He continued: "All the doctors and nurses in the NHS, they do a brilliant job in very difficult conditions and every day they're putting themselves in harm's way night and morning.
"They're doing it with a determination that only we can do and they are continuing to do that and I think we must all say thank you very much to the National Health Service, all of you, not just the doctors and nurses, but everyone throughout the whole system who are doing such a magnificent job."
Asked about his native Yorkshire, Captain Tom said: "I believe that there's no place better than Yorkshire. There never has been and all the people who are missing coming to Yorkshire, they're missing an awful lot of marvellous things and people, because the Yorkshire people have a sense of humour and kindness that not many people have, to the extent that we have."
Captain Tom declared the hospital, which will provide 500 extra beds for Covid-19 patients, open as Paula Lorimer, director of the Harrogate Convention Centre, unveiled a plaque.
The audience, who sat spaced out throughout the auditorium, was made up of partners from different organisations who worked together to make the hospital happen, including clinical and non-clinical workers and the military.
They were asked to stand and applaud as a banner wishing Captain Tom a happy 100th birthday was held up on the stage and the veteran's number one version of You'll Never Walk Alone with Michael Ball was played on the screen.
Celebrities, including Yorkshire favourites James Martin, Paul Chuckle and Jodie Whittaker, also appeared in a montage, giving thanks to the Harrogate facility, which has been set up in less than three weeks.
Health Secretary Matt Hancock also delivered a recorded message in which he offered his "heartfelt thanks". Mr Hancock said: "This is a hospital that nobody would have ever wanted and it is a hospital we hope never to see full.
"But the fact you have been able to make this happen in such a short period of time is a testament to your capabilities, determination and your teamwork.
"And the most important thing about NHS Nightingale in Harrogate is it is a message to everybody across Yorkshire, across the country, that whatever happens we will strain every sinew to make sure the NHS is there for anyone who needs it, from the Prime Minister, who of course needed to go to hospital with coronavirus himself, to every single person in this country.
"So far in this crisis, the NHS has always been there and with these NHS Nightingale hospitals across the country, I'm determined that it always will be."
The extra capacity at the Harrogate hospital adds to other Nightingale hospitals being opened in London, Birmingham, Manchester, Cardiff and Glasgow.
Steve Russell, chief executive of the new hospital, called the project an "extraordinary achievement" and a "vital insurance policy which we hope will not be needed."
He also encouraged people to keep following social distancing rules, and added: "Our doctors, nurses, therapists and other health and social care staff across Yorkshire and the Humber are working incredibly hard to make sure people get the care they need during what is the single greatest challenge in the history of the NHS, but they can't do it alone."
Harrogate Convention Centre's director Paula Lorimer said in a statement this afternoon: "It’s fitting that Captain Tom Moore is our guest of honour opening the Nightingale Hospital for Yorkshire and the Humber at Harrogate Convention Centre.
"The Yorkshire veteran who served in World War Two has become a morale-boosting antidote against the invisible enemy of Covid-19. The grandfather who literally stepped up, walking laps of his garden, has left an imprint on our national psyche. He gives us all a sense of comfort, hope and courage in his resilience and spirit.
This NHS Nightingale Yorkshire and the Humber Hospital is an extension of that spirit. It shows what can be built in a matter of weeks by working collectively to a shared goal. It is no small thing to transform an exhibition and events venue into a fully operational hospital.
"Thanks go to all my team on site, our contractors, and all who we’ve worked so closely with, including the team at NHS Leeds Teaching Hospital, the Army, and Harrogate Borough Council staff.
"To come into work and work all hours - when the instinct and advice is to stay safe and stay home – is to be commended. I’ve said before, all of us will want to be proud of how we responded once this crisis is over, and all who have been part of this effort should feel very proud.
"During the construction period, local businesses, individuals and community groups have also shown huge support to the frontline workers at the convention centre; we thank our town."
Story supplied by Press Association