The broadcasting workers' union, BECTU, said the walkout will be held on 26 February after members voted in favour of industrial action.
The dispute involves job cuts, with unions saying they were determined to avoid compulsory redundancies.
The NUJ said thousands of its members across the UK at the BBC, including radio and TV, will be on strike unless the row is resolved.
Broadcasting officer Paul McLaughlin said: 'We are calling on the BBC to see sense even at this late stage because we have offered sensible solutions to all of the outstanding cases.
'Management intransigence seems to be cause of this dispute.'
The BBC responded by saying: 'We note the decision with regret but we have an obligation to licence fee payers to implement our value-for-money efficiency savings.'
