The corporation's commercial arm, BBC Worldwide, said it is now taking "disciplinary action" over the bungle and has apologised to programme boss Steven Moffat and his team.
Five scripts from the series - starring Peter Capaldi as The Doctor - together with unfinished scenes from six episodes were accidentally placed in a publicly accessible area online.
Fans had to be asked not to share the material on the internet, or post spoilers about what happens. They were also warned that downloading and passing it on would be illegal.
There have been frantic efforts to remove the scripts and scenes - which were still to have special effects added - and a Miami-based server was said last week to have been closed as part of the investigation into what had happened.
A statement issued by BBC Worldwide today said: "We would like to thank Doctor Who fans everywhere for their amazing efforts in helping us contain the recent leaks.
"The mistake was damaging and resulted in the exposure of five scripts and the first six unfinished episodes from Series 8 on a publicly accessible FTP site.
"While there is still a risk that this leak will result in more of this content emerging, so far the impact has been contained to a limited amount of this material through a combination of fans' efforts and the plan that we put in place using new technology and internal manpower to limit any illegal activity.
"We would particularly like to thank the fansite moderators and Doctor Who devotees who have actively protected the programme.
"BBC Worldwide has taken this issue extremely seriously and disciplinary action has been implemented as a result of the incident."
It added: "Our sincere apologies again to Steven Moffat, the cast and production team who toil long hours to make the show in Cardiff, the BBC, and of course the fans who expect so much better."
The new series begins on August 23 but stars and producers are taking the show on a world tour prior to the launch, kicking off in Cardiff.