The cuts will be offset by around 195 new roles, meaning a net reduction of 220 jobs altogether by 2016/17.
James Harding, the BBC's director of news and current affairs, gave details of the cuts to a staff meeting in London.
He said: "Taking nearly £50 million out of a well-run organisation that provides high quality news services that are trusted, relied upon and used by millions of people is an extremely difficult undertaking.
"The challenge is how to make BBC News even better, despite having less money."
The body is already facing strike action in Scotland on the opening day of the Commonwealth Games.
Michelle Stanistreet, general secretary of the National Union of Journalists (NUJ), attacked the latest announcement.
She said: "They plan to get rid of hundreds of staff using licence fee payers' money to cover the redundancy pay-outs and then immediately hire in a load more. You couldn't make it up."
Gerry Morrissey, general secretary of the technicians' union Bectu, said he understood the posts would go before any of the new jobs were filled.
He warned of industrial action if the BBC went ahead with cutting the jobs first.
Mr Harding said: "We are living through a period of extraordinary change in news media.