Union leaders said the biggest job cuts in BBC history threaten to destroy the heart of the corporation.
In a joint statement, the National Union of Journalists, Amicus and Bectu said: "We are committed to working together to oppose at all levels the effects of the director-general's savaging of staff in the biggest cuts in BBC history.
"His announcements showed high-handed disregard for the future of thousands of staff, and threatened the very heart of the BBC."
But director-general Mark Thompson insisted the losses are "the right price to pay" if the BBC is to remain "the greatest force for cultural good on the face of the earth".
The BBC is hoping to save £320m per year, which will be put back into programme-making.
An initial 2,900 job losses have been announced, with further cuts expected in the New Year. The vast majority of posts will go from administrative departments, including HR, finance, marketing, training and legal services.
In addition to the losses, 1,800 jobs are to be moved from London to Manchester.