There's a Guardian article here speculating about how he did it, with a poll.
The theories in the Guardian poll are:
34% Split screen trick photography
11.4% Numbers projected onto the blank balls
5.1% 'Writing recognition' software
5.8% The numbers didn't actually exist and we were hypnotised to think he got it right (I must confess I didn't actually notice if they were the right numbers - rely on others to check)
4.1% The podium was swapped
18.5% It was filmed in reverse and played back as if in real time (I don't think this is possible, but it's the solution he has hinted at)
20.8% Debbie McGee wearing a cloak of invisibility
My son thinks DB spent the past year recording 50 or 60 thousand 'reveal the balls' scenes, and the correct one was spliced onto the studio feed. Although there are many more combinations than that, this gave him a better than evens chance, and if he'd missed one number he would have talked his way out of it.
I think split screen trick photography is a rubbish method, and I hope he didn't use that. I think swapping the podium during the camera pan is an elegant solution. At the time it happened I thought there might be an LCD display built into the balls, and I see the first comment on the Guardian blog suggests that.
DB says he's going to reveal how he did it on Friday. A further question is whether he's likely to tell the truth about the method he used. I think he's more likely to make something up: his 'revelations' are generally fake.