BBC shows such as Doctor Who and EastEnders are to be made available on-demand after the BBC's iPlayer service was given the green light.
The iPlayer will allow viewers to catch up with Doctor Who
The service - which will launch later this year - allows viewers to watch programmes online for seven days after their first TV broadcast.
Episodes can also be downloaded and stored for up to 30 days.
The BBC Trust gave the iPlayer the go-ahead after consultations with members of the public.
About 10,500 individuals and organisations responded to the public value test after the trust gave its provisional approval in January.
As a result, the trust amended two conditions it had earlier imposed on the BBC's plans.
It had earlier called on the corporation to scale back plans to let downloaded "catch-up" episodes remain on users' hard drives beyond seven days.
iPlayer will allow viewers to catch up on TV programmes for seven days
Some TV series can be downloaded and stored for 30 days
Viewers will be able to watch shows streamed live over the internet
Users will not be able to download programmes from other broadcasters
Classical recordings and book-readings are excluded from iPlayer
Now all episodes of some series will be made available until a week after transmission of the final instalment. But this will only apply to 15% of all content offered by the service.
And the storage window for TV catch-up over the internet has been set at 30 days from the day of download.
The trust also called for revised editorial guidance on the type of series which can be included.
BBC director general Mark Thompson said he was "delighted" with the decision.
But he took issue with a decision that classical music downloads could not feature in the service.
"Our research suggests that classical music audiences would wish to download classical music programmes from the BBC and to listen to them on their terms, free at the point of use," he said.
The iPlayer computer application will only be initially available to those with Windows PCs in the UK.
But the trust has asked the BBC to ensure that the iPlayer computer application can run on different systems - such as Apple Macs - within "a reasonable time frame".
Viewers can catch up with EastEnders for seven days after each episode
Earlier this month BBC Future Media boss Ashley Highfield said the corporation was committed to rolling out the iPlayer on Windows PCs first of all, and then cable TV services, Apple Macs, and eventually Freeview boxes.
But the BBC said it could not commit to a two-year deadline to achieve this goal, saying it was up to the third parties concerned.
However, the BBC Trust said it would audit the BBC's progress against this objective every six months to ensure that members of the public not using Windows PCs would not be disadvantaged.
BBC trustee Diane Coyle said: "We are delighted so many people responded to the consultation and thank everyone who participated for their contribution.
"The consultation has demonstrated considerable public support for the on-demand proposals.
"Thanks to the thorough assessment through the public value test, and with the modifications which resulted from the test and the consultation, the trust is satisfied that the BBC's new on-demand services will create significant public value with limited market impact."