The network has broadcast radio programming to the country for many years, and now plans to make three pay-TV channels available to viewers there.
The Guardian reports that children's favourites including Teletubbies, In the Night Garden and Mister Maker will air on the pre-school channel CBeebies.
Doctor Who and The Graham Norton Show will be broadcast on BBC Entertainment, and 24-hour news will be broadcast on BBC World News.
Peter Horrocks, the BBC's director of global news, said: "For many years, the BBC has delivered accurate, impartial international radio services to the Burmese people, serving as a vital lifeline service to Aung San Suu Kyi and those across the country.
"I'm so pleased that the BBC is now able to take the next step forward with the country to offer that same impartial news via television as well. It is a great sign of progress for Burma and I'm honoured for the BBC to play a role in opening the country up to the world."
All three TV channels, together with BBC World Service in Asia in English, will launch on Forever Group's pay-TV platform on January 1.
In 2010, the BBC was in danger of withdrawing the World Service from Burma due to projected budget cuts. Burmese democracy activist Aung San Suu Kyi subsequently revealed how she would look forward to Dave Lee Travis's show on the network while under house arrest, saying it "made my world much more complete".