Eccleston has admitted he has decided to leave over fears of becoming typecast as the Doctor, as previous actors have done.
Eccleston was already the star of hit movies 'Shallow Grave', 'The Others', 'Gone in 60 Seconds' and '28 Days Later', as well as TV hits such as 'Cracker' and 'The Second Coming'. He said he believed the roles would dry up if he continued filming 'Doctor Who.'
The first series took almost a year to make and Eccleston described the filming as hard work and "gruelling".
The BBC has confirmed it is talks with 'Casanova' actor David Tennant as a possible replacement for Eccleston.
A spokesman for the BBC said: "Chris will not be returning to Doctor Who. We are in discussions with David Tennant about taking the role."
There are other names also in the running for the role and Ladbrokes has opened up betting on who will replace Eccleston. The bookmakers has named Tennant as hot favourite at 1/10. Other contenders include Bill Nighy, Sean Pertwee, Eddie Izzard and The League of Gentleman's Mark Gatiss.
Ladbrokes spokesman Warren Lush, said: "Public demand has forced us to produce a long list of possible doctors despite the fact that David Tennant is so hotly tipped for the role. There's even a real doctor in the betting but Harry Hill is seen as a 1000/1 chance."
"Before Eccleston took the role the money was for Alan Davies and Eddie Izzard and they have to be seen as possible contenders again. We certainly don't rule out Eccleston changing his mind and appearing in the second series, we only offer 2/1."
The future of Billie Piper as the Doctor's assistant Rose is also hanging in the balance, although some reports say she might well be back. The former pop star and soon-to-be ex-wife of Chris Evans has made it clear she would be interested in a high-profile acting career in Hollywood if the opportunity were to arise.
One person who is planning to stay put is writer Russell T Davies, who wrote the new series and is credited with reviving the show, which is set to see the return of the Daleks. Davies will be penning the 60-minute Christmas special.
Russell said it was fantastic news that the second series had been commissioned.
"It's been a tense and jittery time because the production team has been working on plans for series two -- scripts are being written already -- without ever knowing if it would ever get made. We could all have ended up unemployed. But now we can put all those plans into action and get going," he said.
'Doctor Who''s first terrestrial outing pulled in a peak of 10.5m viewers on Saturday night, representing a 44.3% share, leaving ITV1's 'Ant and Dec's Saturday Night Takeaway' with 8.5m viewers, or a 35% share despite securing England captain David Beckham as a special guest.
BBC drama controller Jane Tranter has admitted that she was not expecting the first episode to pull in the 9.9m average and 10.5m peak ratings.
"I told myself I'd be completely and utterly thrilled if it got 6.5m, but there was a little voice inside whispering '4.5m'," she said.
The odds on Dr Who winning the weekend's ratings battle with Ant and Dec have been cut from evens to 5/6. We now offer 5/6 for both programmes, we are unable to split them.
"The battle between the BBC and ITV this weekend looks too close to call," said Lush.
Ladbrokes: next permanent Dr Who?
1/10 David Tennant
12/1 Alan Davies
14/1 Bill Nighy
16/1 Sean Pertwee
16/1 Eddie Izzard
16/1 Mark Gatiss
20/1 Richard E Grant
25/1 David Thewlis
33/1 Alan Cumming
40/1 Jonathan Pryce
40/1 David Warner
50/1 Chiwetel Ejiofor
80/1 Jon Culshaw
500/1 Tom Baker
500/1 Colin Baker
500/1 Sylvester McCoy
1000/1 Paul Daniels
1000/1 Roger Daltrey
1000/1 Neil Fox
1000/1 Johnny Vegas
1000/1 Harry Hill
1000/1 Graham Norton
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