An unexpected increase in the number of households saying they do not watch live TV so do not pay for a licence has been blamed for the shortfall.
Many cuts are to come from professional and support areas, while management structures will be streamlined.
BBC director general Tony Hall says this will save around £50m a year so more cuts will come.
Lord Hall said the BBC was facing “difficult choices” because of the tough financial climate.
He said more than one million fewer people had a television set than was predicted in 2011, when another round of efficiency savings were implemented, so extra savings had to be found.
“Despite the progress already made, and the realities of the licence fee being frozen for seven years, a new financial challenge means additional savings must now be found,” he said.
He added decision-making had become too complicated in recent times, as new services have been introduced, and that he wanted to cut these back to make things simpler, which “inevitably would lead to fewer decision-makers”.
Professional and support departments such as IT, human resources and engineering will be looked at closely to see where there is duplication, with the possibility of merging divisions across the BBC and its commercial arm, BBC Worldwide.
In announcing more than 1,000 jobs cuts, Lord Hall said he recognised “this is a tough message”.
He said the BBC was already making £1.5bn in savings every year, but because of the shortfall in licence fee income, more needs to be done.
The four key areas for making the savings are:
- Merging divisions, bringing together teams in BBC and BBC Worldwide
- Cutting out management layers, reducing management levels from 10 to seven
- Reducing management roles, bringing down the number of senior positions
- Simplifying procedures in professional areas including legal, marketing and finance