Smith, who will take over from David Tennant when he leaves the show at the end of 2009, was a massive outsider to take the role in the week leading up to the announcement, with listing his odds at 31-1.
But more than 24 hours before the BBC named Smith as the new Doctor, his odds dropped down to 1-3, making him favourite.
Paddy Power's odds on Smith also shortened, dropping from 33-1 to 10-1.
The identity of the new Doctor was then revealed on a special edition of 'Doctor Who Confidential', which BBC One broadcast on Saturday January 3.
The broadcaster said it would not be investigating the possibility of a leak as it "has no knowledge of anyone betting on the outcome of the identity of the eleventh Doctor".
A BBC source told the Evening Standard: "It does look like somebody knew and went on the betting exchanges, but this was not necessarily someone from the BBC.
"It could have been an individual connected to the actor, through his associates or a friend, or even people working on the promotional material -- who knows?
"If the bookmakers feel that there was some suspicious betting going on then it is up to them to investigate."
Smith was awarded the role ahead of early favourite Paterson Joseph, who has appeared in 'Peep Show' and 'Green Wing'.
The 26-year-old will be the 11th Time Lord and will be seen in the forthcoming fifth series due to be broadcast in 2010.
He has recently completed work on 'Moses Jones' for BBC Two, in which he plays the lead role of Dan Twentyman.
Smith has also appeared alongside Billie Piper in Phillip Pullman's period detective stories, 'The Ruby In The Smoke' and 'The Shadow In The North', and was the lead in the BBC Two series 'Party Animals'.
He said: "I feel proud and honoured to have been given this opportunity to join a team of people that has worked so tirelessly to make the show so thrilling.
"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.
"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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