The cuts will be offset by around 195 new roles, meaning a net reduction of 220 jobs.
James Harding, the BBC's director of news and current affairs, gave details of the cuts to a staff meeting in London, saying: "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."
Michelle Stanistreet, general secretary of the National Union of Journalists (NUJ), attacked the 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.
Journalists and technicians are already going on strike for 12 hours next Wednesday, to coincide with the opening ceremony of the Commonwealth Games, in a row over pay.