Outgoing director general Tim Davie, who is leaving the BBC in April, told staff about the savings on Thursday.
A BBC spokesperson added: “Over the last three years we have delivered more than a half a billion pounds worth of savings, much of which we’ve been able to reinvest into our output across the BBC.
“In a rapidly changing media market, we continue to face substantial financial pressures.
“As a result we expect to make further savings over the next three years of around 10% of our costs.
“This is about the BBC becoming more productive and prioritising our offer to audiences to ensure we’re providing the best value for money, both now and in the future.”
The announcement comes as the BBC negotiates with the government about its future, and that of the licence fee, ahead of the renewal of its royal charter at the end of 2027.
The government recently launched a consultation to ask the public for their views about the future of the BBC and how it should be funded.
The corporation gets most of its income from the licence fee, but the number of TV licences sold has been declining in recent years.
The BBC has said it accepts that the licence fee needs reform, but that any changes must “safeguard the BBC as a universal public broadcaster”.