The Doctor Who actor and former member of the theatre joins as the NYT prepares for the Olympic and Paralympic Team welcome ceremonies.
"I think from my experience the thing about the NYT is that you learn through practice," Smith said.
"You're out there on a stage, you're doing a play, you're being directed, you're turning up for rehearsals every day and working as you would work in a professional rehearsal room."
He added: "It completely transformed my life. No understatement. I'm proud to be part of it still and proud to be the organisation's newest Patron, as I care very deeply about it."
NYT artistic director and CEO Paul Roseby added: "We're all thrilled at the National Youth Theatre to announce that Matt Smith is the latest recruit to our illustrious list of Patrons, as we get ready for our Olympic and Paralympic performances.
"Matt is a perfect role model for the latest generation of brave new talent. Raw, fearless and a passion for theatre is something that doesn't just sum up our company but also the wonderful Matt Smith.
"As we continue to operate in challenging economic times, like everyone in the arts, it's always good to have a Doctor in the house."
Smith said of the NYT's collaboration with the Olympics: "It was an honour to be a torchbearer and carry the Olympic flame in Cardiff, and it's a wonderful thing that National Youth Theatre will be representing Great Britain and welcoming the world to London with the Team Welcome Ceremonies.
"I've just met the NYT cast and the levels of enthusiasm and commitment was nothing short of inspiring. I think it's a great day for the National Youth Theatre and I know that they'll deliver something of the highest and most professional quality, because that's what they do."
Smith joined the NYT in 2002 and starred as Thomas Beckett in its Murder in the Cathedral at London's Southwark Cathedral and Basoon in The Master and Margarita at the Lyric Hammersmith.