Negotiations for the BNP to take part in the programme, which is presented by David Dimbleby, are already at an advanced stage.
Leader Nick Griffin is most likely to appear on the show after he was elected a Member of the European Parliament earlier in the year.
As the BNP now have two seats at Strasbourg, the BBC said that it was "right" for them to be represented on Question Time.
"The BBC is obliged to treat all political parties registered with the Electoral Commission and operating within the law with due impartiality," said a BBC spokeswoman.
"By winning representation in the European Parliament at the recent elections, the BNP has demonstrated evidence of electoral support at a national level.
"This will be reflected in the amount of coverage it receives on BBC programmes such as Question Time. That is consistent with the approach taken at previous elections, for instance, when UKIP and the Greens won European seats."
Welcoming the decision, a BNP spokesman told The Guardian: "Obviously it's good news. Of late, a large proportion of Question Time has been devoted to assaults on the BNP, so it's rather welcome that we are allowed to defend ourselves."
However, the decision to give a platform to the controversial political party could result in other guests declining to take part in the programme. Campaigners are also thought to be preparing protests to force the BBC to cancel the invite.
Gerry Gable, publisher of anti-fascist magazine Searchlight, told The Daily Telegraph that bringing the BNP on to the popular show would only "add legitimacy to them".
He added: "People will turn on and see him as a member of a legitimate panel and think 'they must be OK'."
However, former Downing Street communications director Alastair Campbell has backed the decision and also urged ministers to seize the opportunity to challenge the BNP.
Writing on his internet blog, Campbell said: "Griffin's world-view is repulsive, his political methods equally so, but as I said at the time of the European elections, the BNP have to be taken on and beaten in argument.
"At local level, where the BNP have been elected, other parties have had no choice but to sit down and debate with them."
The Conservatives have already indicated that they would be prepared to debate with the BNP to "show them up for the nasty party that they are".