The 24-hour walkout by members of the National Union of Journalists is in protest at compulsory redundancies, including staff posts in Scotland.
It began at midnight when Michelle Stanistreet, NUJ general secretary, led journalists out of the building at the BBC's central London studios.
Picket lines were being mounted outside BBC studios and offices across the UK, including at Pacific Quay in Glasgow, and the union said the strike was being well supported. More than 100 people were involved in a picket in Glasgow.
James Cook, Scotland correspondent for BBC News and an NUJ member, said cuts are already affecting programming and job losses are being pushed through too quickly.
He said: “It is intellectually incoherent to argue that you can make cuts this deep while continuing to increase the number of programmes and keep up the quality.
“The strength of numbers here at Pacific Quay underlines the feeling among staff.
“It’s not just about cuts to colleagues’ jobs, people being forced, it’s also about the impact on the licence payer.”
BBC radio and TV news programmes have been badly affected by today`s walkout, with the flagship Radio 4 Today programme replaced with pre-recorded features. National and regional TV news bulletins were also hit.
The Today programme was not broadcast at its usual time of 6am, and BBC TV's breakfast news, missing its normal bulletins from Scotland, was largely missing, with old episodes of Bargain Hunt and Escape to the Country being shown instead.
The corporation was covering the strike by its own staff, while also broadcasting repeated apologies to viewers for the disruption.
The NUJ said it had not ruled out further industrial action, but was calling for more talks over compulsory redundancies, and a moratorium on job cuts until new director general Tony Hall takes over in April.
Ms Stanistreet, said: "NUJ members across the BBC are taking action to defend jobs and quality journalism at the corporation. They are angry and frustrated at the poor decisions being taken at the top of the BBC - decisions that are leading to journalists being forced out of their jobs and quality journalism and programming compromised.
"Instead of making sure that the redeployment process works properly in all areas of the BBC, managers are prepared to waste public money on needless redundancies and sacrifice the livelihoods of experienced and talented journalists, at the same time as advertising other jobs externally.
"It's particularly disappointing that the BBC has failed to engage meaningfully in attempts to resolve this dispute - an abdication of responsibility for a public service broadcaster."
TheBBC said it was "disappointed" with the industrial action, adding that it would not alter the fact that it has to make "significant" savings.
The NUJ said its members across the BBC - in Scotland, in BBC South, the Asian Network, Newsbeat, Five Live, the World Service and English Regions - were at risk of compulsory redundancy.
A BBC spokesman said: "We understand how frustrating and difficult situations involving redundancies can be, but it is disappointing the NUJ have chosen to take this action.
"We are working hard to ensure that we succeed in getting staff redeployed wherever we can and will continue to work with the unions to ensure that their members receive the right redeployment support."
The BBC, which is cutting around 2,000 jobs under its so-called delivering quality first programme, said 554 employees had left as a result of voluntary redundancy, 186 had been redeployed, and there have been 153 compulsory redundancies.
A BBC spokesman added: "We are disappointed that the NUJ has gone ahead with today's strike and apologise to our audience for the disruption to services. Unfortunately industrial action does not alter the fact that the BBC has significant savings targets and as a consequence may have to make a number of compulsory redundancies.
"We have made considerable progress in reducing the need for compulsory redundancies through volunteers, redeployment and cancelling vacant positions and we will continue with these efforts."