National Union of Journalists General Secretary Jeremy Dear said about 84 percent of BBC employees that are its members voted in favour of the strike.
He said the vote indicated the "huge anger" within the BBC over the cuts proposed by Director General Mark Thompson.
Employee representatives will meet over the coming days to decide on what action to take, while talking to the BBC to avert strike action.
The BBC plans to cut around 4,000 jobs over the next three years.
It has remained schtumm on the development thus far. ยต