Unions have called for renewed talks with the BBC after journalists and broadcasting workers voted to strike in protest at plans to cut 3,780 jobs.
Unions want to disrupt as many programmes as possible
Members of the Bectu and NUJ unions voted in favour of a walk-out - probably a 12- or 24-hour stoppage between mid-May and early June.
The unions will meet on Thursday to plan the industrial action.
The BBC said it was "disappointed" at the result and "would prefer... constructive discussions".
The BBC is expected to try to minimise disruption if the strike goes ahead but Bectu has said previously they would seek "black screens and dead air".
Bectu said it would "do everything we can to make sure any programmes that are going out are badly affected".
News and live broadcasts could be hardest hit - raising fears that it could hit events such as the FA Cup Final, on 21 May.
Director general Mark Thompson says savings will go into new shows
The corporation said: "Given the scale of the changes that the BBC needs to make, and that the unions have not allowed us to talk to them in order to address their concerns, we are not surprised by the ballot result."
Half of Bectu's 5,000 members at the BBC voted, with 77.6% in favour of striking.
Among NUJ members, 83.9% were in favour after almost two thirds of the union's 3,500 BBC staff members cast their ballots.
"This is a ringing endorsement of the action of the joint unions and shows the determination of our members to stop these damaging job cuts," Bectu official Luke Crawley said.
NUJ General Secretary Jeremy Dear said the result was "a reflection of the huge anger at the scale and impact" of director general Mark Thompson's cuts.
"The cuts package is badly thought out, doesn't add up, will do irreparable damage to quality and standards and has been soundly rejected by staff," he said.
BBC media correspondent Torin Douglas said: "The BBC has been saying all along that the cuts are necessary to make the BBC more efficient."
Mr Thompson has argued that the proposed job cuts would put more than £350m a year back into programme-making.
He maintains that most of the job losses would be achieved through staff turnover and voluntary redundancies.