An audience of 16 and 17-year-olds will have the chance to air their thoughts and quiz a panel of politicians and experts in the one-off broadcast from Edinburgh on June 13.
The move reflects the influential role teenagers could play when Scots go to the polls to determine the fate of the union next autumn.
Proposals to allow 16 and 17-year-olds a vote in the independence referendum are set to be rubber-stamped by the Scottish Parliament later this year.
Campaigns on both sides of the independence debate welcomed the special programme and agreed to put forward spokesmen for the panel if approached by the BBC.
Little is known about the way teenagers will vote come 2014. Earlier this year a mock referendum held by Glasgow University returned a resounding defeat for the pro-independence cause in the first student poll of its kind.
When asked "Should Scotland be an independent country?" – the same question to be put to voters next year – 62% of the 2500 students who voted said no.
Question Time, one of the BBC's flagship current affairs programmes, often attracts more than three million viewers and allows audience members to share their own views and challenge panelists.
In February the programme was broadcast from Stirling with a panel including Michael Moore MP, Humza Yousaf MSP, Lord Falconer, Mary Macleod MP, and Sir Brian Souter, chief executive of Stagecoach Group.
Discussing the one-off teenage audience, a spokesman for Yes Scotland said: "We very much welcome this move by the BBC. We were delighted when the Scottish Parliament agreed to extend the franchise for the referendum to include 16 and 17-year-olds.
"They will play an important role in the debate over the next 17 months.
"It is only right and fair that the views of young people are expressed and listened to as we decide the future fate of our country.
"Yes Scotland has never taken a view that including 16 and 17-year-olds in the franchise would influence the vote one way or the other. It was simply the right democratic thing to do."
Earlier this year Yes Scotland appointed Ellie Koepplinger, a 16-year-old student from Maryhill, Glasgow, to the campaign's advisory board alongside key politicians and public figures including First Minister Nicola Sturgeon and actress Elaine C Smith.
A spokesman from Better Together said of the special programme: "We fully support every opportunity to have young people involved in the debate on Scotland's future.
"We set up our Youth Representative programme earlier this year in order to make sure that young people were able to get involved in the campaign.
"Already we have more than 150 young people organising and attending events right across Scotland. We aim to recruit hundreds more in the next few months."
"Young people tell us that they cannot understand why you would want to cut ourselves off from our closest neighbour at a time when the world is breaking down barriers. They tell us that we are stronger when we work together."
A poll published last month found 29% of Scots aged 16 to 24 would vote yes in the independence referendum, with 52% of respondents voting no.
A BBC spokesman said the debate would touch on a range of issues including the independence vote, and said teenagers could sign up to attend via the Question Time website.
He added: "We decided to have an audience of 16 and 17-year-olds because the referendum on independence next year will be the first time this group of young people have a vote. We will announce the panel nearer the time."