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It is a continuation of the original show and TV Movie. The new show has made references to the original show by having the characters Sarah Jane Smith, K9 and the Brigadier (in spin-off show 'The Sarah Jane Adventures) returning thus proving that it is a continuation. In the episode 'The Next Doctor' we briefly saw images of all the previous Doctors, including all the Doctors from the original series, which furthermore backs this up. And in the series three two parter "Human Nature/Family of Blood" John Smith's "Journal of Impossible Things" freatures a sketch drawing of all the previous Doctor's from the classic series. The original show has also been specifically referenced in other episodes of the new series such as 'School Reunion', 'The Fires of Pompeii', 'The Poison Sky' and 'Journey's End'. Also the mini-charity episode 'Time Crash'(which is considered canon) features the Fifth Doctor from the original series.
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