Smith, 28, who has been in the role since 2010, said it had been "an honour" to play the part.
He said: "Doctor Who has been the most brilliant experience for me as an actor and a bloke, and that largely is down to the cast, crew and fans of the show.
"I'm incredibly grateful to all the cast and crew who work tirelessly every day, to realise all the elements of the show and deliver Doctor Who to the audience. Many of them have become good friends and I'm incredibly proud of what we have achieved over the last four years."
Smith also paid tribute to the programme's producer, Steven Moffat, whose "varied, funny, mind bending and brilliant scripts has been one of the greatest and most rewarding challenges of my career". He said: "It's been a privilege and a treat to work with Steven, he's a good friend and will continue to shape a brilliant world for the Doctor.
"The fans of Doctor Who around the world are unlike any other; they dress up, shout louder, know more about the history of the show (and speculate more about the future of the show) in a way that I've never seen before, your dedication is truly remarkable.
"Thank you so very much for supporting my incarnation of the Time Lord, number Eleven, who I might add is not done yet, I'm back for the 50th anniversary and the Christmas special."
Smith, who recently made his directorial debut with Cargesee for Sky Arts, has spoken about ambitions for a film-making career.
He became the eleventh, and youngest, incarnation of the Time Lord when he was unveiled as the new Doctor, replacing David Tennant who had taken over from Christopher Eccleston in 2005. It is not yet known who will replace Smith as the Doctor. His most recent on-screen companion, played by Jenna-Louise Coleman, will stay with the show.
Rumours of Smith's departure from the series sparked speculation over who will be his replacement when the Doctor is regenerated in a new form once more. Favourites include Homeland star Damian Lewis or that Tennant may make a return. idts
Mr Moffat said: "Every day, on every episode, in every set of rushes, Matt Smith surprised me: the way he'd turn a line, or spin on his heels, or make something funny, or out of nowhere make me cry, I just never knew what was coming next.
"The Doctor can be clown and hero, often at the same time, and Matt rose to both challenges magnificently. And even better than that, given the pressures of this extraordinary show, he is one of the nicest and hardest-working people I have ever had the privilege of knowing.
"Whatever we threw at him - sometimes literally - his behaviour was always worthy of the Doctor.
"But great actors always know when it's time for the curtain call, so this Christmas prepare for your hearts to break, as we say goodbye to number Eleven. Thank you Matt - bow ties were never cooler.
"Of course, this isn't the end of the story, because now the search begins. Somewhere out there right now - all unknowing, just going about their business - is someone who's about to become the Doctor.
"A life is going to change, and Doctor Who will be born all over again. After 50 years, that's still so exciting."
Source / BBC UK announcement
I'm updating this post in case news other than Matt leaving arise.