Viewers can tune into the channels online via bbc.co.uk, using a computer or other portable devices.
Jana Bennett, director of BBC Vision, said: "The launch of BBC One and BBC Two online completes our commitment to make our portfolio of channels available to watch on the internet.
"From 27 November licence fee payers will be able to watch BBC programmes, live, wherever they are in the UK on their computers, mobile phones and other portable devices.
"Through iPlayer and series stacking, they'll have the option to catch up with them later."
Video on the channel sites is restricted so it cannot be viewed from outside the UK.
However, the BBC said anyone in the UK watching or recording TV as it is being simulcast on any device -- including mobiles, laptops and PCs -- must, by law, be covered by a valid TV Licence.