The National Union of Journalists (NUJ) said its members at the corporation will walk out on February 18 and launch a work to rule from Friday.
The action will go ahead unless talks between the two sides this week resolve a dispute over jobs.
The NUJ said the BBC was planning around 30 compulsory redundancies, affecting areas including BBC Scotland, the Asian Network, the World Service and English regions.
Michelle Stanistreet, NUJ general secretary, said: "The BBC is prepared to waste public money on needless redundancies rather than secure redeployment opportunities for those at risk.
"This demonstrates the significant failures of some managers to uphold key aspects of the redeployment agreement, let alone the spirit of the deal.
"In the meantime we have meetings planned with the BBC and we want to engage in meaningful negotiations to resolve this dispute. I hope common sense prevails and a sensible solution is agreed which will mean that strike action is not necessary."
A BBC spokesperson said: "We understand how frustrating and difficult situations involving redundancies can be, but it is disappointing the NUJ have chosen to take this action.
"We are working hard to ensure that we succeed in getting staff redeployed wherever we can and will continue to work with the unions to ensure that their members receive the right redeployment support."