Aged 26, he will be the youngest ever actor to play the iconic role. His credits include political drama Party Animals and The Ruby In The Smoke, opposite former Who companion Billie Piper.
Of his casting, Smith said: "I'm flabbergasted. I haven't slept really! [Doctor Who] is an iconic part of our culture, and now I'm taking that on. It's nervewracking. Exciting. Exciting."
Smith will replace Tennant at the end of four Doctor Who specials, the last of which will air at the start of 2010. He will then go on to helm a full fifth series alongside a new companion, who is yet to be named.
Steven Moffat, who takes over from Russell T Davies as executive producer following the specials, said: "The Doctor is a very special part, and it takes a very special actor to play him. You need to be old and young at the same time, a boffin and an action hero, a cheeky schoolboy and the wise old man of the universe.
"As soon as Matt walked through the door, and blew us away with a bold and brand new take on the Time Lord, we knew we had our man.
"2010 is a long time away but rest assured the 11th Doctor is coming – and the universe has never been so safe."
Tennant announced his decision to quit the long-running series in October 2008, saying that he did not want to "outstay [his] welcome". By the end of his tenure, Tennant will have appeared in three full-length series and eight specials.
"David Tennant has made the role his own, brilliantly, with grace, talent and persistent dedication. I hope to learn from the standards set by him," added Smith.
"The challenge for me is to do justice to the show's illustrious past, my predecessors, and most importantly, to those who watch it. I really cannot wait."
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