“For audiences, the job in hand now over the next three or four months is to work through how we make those changes without damaging the services that we know are critical to the BBC across radio and television and online,” he said.
He also acknowledged that the job cuts would be “really difficult news” for staff.
Philippa Childs, head of broadcasting union Bectu, warned that “cuts of this magnitude” would be “devastating for the workforce and to the BBC as a whole”.
The BBC currently has about 21,500 full time equivalent employees.
In an email to staff on Wednesday, Talfan Davies said: “As you know, the BBC is facing significant financial pressures, which we need to respond to with pace.
“Put simply, the gap between our costs and our income is growing. This is being driven by a number of factors: production inflation remains very high; our licence fee and commercial income is under pressure; and the global economy remains turbulent.”
He also imposed tighter controls on spending on recruitment, travel, management consultancies, and attendance at conferences, awards and events.