The stunning setting of the Glasgow art gallery and museum will play host to the First Minister and leader of the Better Together campaign in the crucial programme, which will be screened prime-time across the UK.
It will also be available in 100 other countries.
The debate is the second in the run up to the poll on September 18.
The BBC's promised looks set to eclipse STV's viewing figures of 1.2million in Scotland, with a further 500,000 following on the channel's website across the UK. The website had struggled to cope with the surge in demand.
Experienced presenter Glenn Campbell will present the 90 minute debate that will be held before an audience of 200 who will put the representatives of the opposing campaigns in the referendum on the spot as they seek answers about the choice Scotland faces next month.
Audience members will be selected by polling and research consultancy, ComRes, to reflect a broad balance of views and their questions will feature prominently in the programme, Scotland Decides: Salmond versus Darling, which will be shared as a simulcast with other broadcasters and media outlets including newspapers.
BBC One Scotland will air the programme from 8.30-10pm. Viewers in other parts of the UK will be able to catch it on BBC Two, including HD channels. From midnight on August 25, it will also be shown across the UK on BBC One.
It will also air on the BBC News Channel and BBC World News which is available in over 100 countries. Radio Scotland and Radio Nan Gaidheal will also simulcast the debate.
The programme marks the latest stage of the BBC's extensive coverage of the historic referendum across all platforms.
John Boothman, Head of News and Current Affairs, BBC Scotland, said: 'Interest among the voting public in this historic debate has consistently been high and our wide range of programming over many months has underlined our commitment to ensure audiences are as well informed as they can be about all the key issues.
'Debates on both radio and television, from across the country, have been a central part of our programming and they have given audiences the opportunity to interrogate representatives from both sides of the argument.
'We expect the audience at the Kelvingrove Art Gallery and Museum and those watching and listening at home will be in for an absorbing evening's debate on the referendum's burning questions.'
He added: 'Clearly the referendum is of huge historic significance and, as part of our public service remit, we are delighted we can offer live streams of the debate to non-BBC media outlets in Scotland and elsewhere in the UK.'