The move is designed to improve transparency and openness at the authority.
Westminster City Council director of comms and strategy Alex Aiken said: 'We are committed to being open and transparent to demonstrate to our residents how we spend their hard-earned money.
'While we have previously allowed filming at our council meetings with the chairman's discretion, with the huge rise in social media and new modern recording equipment it's right we now update these rules to incorporate live blogging, Twitter and Facebook.'
Council chiefs said with the use of smaller video cameras and the rise of social media, it was important the public could use modern comms methods to access and record meetings.
It follows reports that some bloggers were stopped from using Twitter or filming during public meetings at local authorities in London and Manchester.
In February local government minister Bob Neill MP sent a letter to all council leaders saying that citizen journalists and bloggers should have the same access to council meetings as mainstream media to scrutinise the work of local government.