BBC Three will be moved online next year - a change that could potentially lead to the loss of more than half a million viewers.
A financially-motivated proposal to move the channel online was provisionally approved by the BBC Trust in June and its fate has now been formally sealed by the broadcaster's governing body.
The trust's final decision will see the partial demise of the channel that brought hit shows including Gavin And Stacey and Don't Tell The Bride to TV viewers.
It will begin to run online in February, with the TV channel remaining in place until March to direct viewers to its new home on the internet.
Trustees found there was clear public value in moving BBC Three online as evidence shows younger audiences are watching more on the web and watching less linear TV.
But a public value assessment (PVA) found that 80% of the "uniquely-reached" BBC Three audience would "simply be lost".
Clarifying the 80% figure, a BBC Trust spokeswoman said: "It's not the case that 80% of BBC Three's audience will be lost under the plans announced today. What we said was that, without anything to replace it, 80% of the 924,000 people who only watch BBC3 and no other BBC TV could be lost.
"However, the plans we have approved ensure that specific programmes for younger audiences will continue on both BBC Three online and in dedicated slots on BBC One and BBC Two."
The PVA also found the move offered low value for money because of the smaller audience but recognised the closure would generate a net saving of £30 million per annum.
The trust acknowledged the strength of public opposition to the closure of the TV channel but said the long-term future of broadcasting "seems likely to be online".
It recognised that the move online is earlier than the BBC Executive would "ideally have planned".
It also noted that the loss of the linear platform "may result in less exposure for new shows and that this could make it difficult for the BBC to attract and nurture new talent".
A condition requiring BBC Three programmes to be broadcast on BBC One and Two has been strengthened so all BBC Three long-form programmes must be broadcast on the two channels, and they must be broadcast at a variety of times across the schedule and throughout the UK.
A condition requiring BBC One and Two to offer programmes specifically aimed at younger audiences, including BBC Three programmes, requires the channels to offer distinctive programmes designed for younger audiences.
A service review will be conducted within 18 months, assessing the progress of the new online BBC Three and the effectiveness of the conditions the trust has imposed.
The trust could then consider imposing quotas or formal targets if it considers that performance against the conditions has been unsatisfactory.
Meanwhile, the trust has approved plans to extend the hours of CBBC to 9pm and to develop iPlayer beyond a catch-up service, to include online-first and third party content.
But it formally rejected the BBC's proposals for a BBC One +1 channel on the basis of limited public value.
Damian Kavanagh, controller of BBC Three, said: "Today is just the beginning for BBC Three and our plans to transform our offer for young people.
"We have lots of new content coming in 2016 and exciting new ways of delivering it in development.
"We will now set about launching a digital first BBC Three in early 2016."
Jono Read, from the Save BBC3 campaign, said: "The decision is bitterly disappointing and it is a very sad day for the future of the BBC."