It will be an assembly dominated by MPs from Aung San Suu Kyi's National League for Democracy (NLD), which won 80% of elected seats in November's poll.
But a quarter of all seats are reserved for the military, which also retains key ministries under the constitution.
One of the new parliament's first jobs will be to choose a new president.
Outgoing leader Thein Sein steps down at the end of March, but Ms Suu Kyi, who spent 15 years under house arrest, is constitutionally barred from standing because her sons are British not Burmese.
She has previously indicated that she will seek to exert influence through the new leader.
But there has been speculation that a deal may have been done with the military to allow her to take the job, says the BBC's Jonah Fisher in the capital Nay Pyi Taw.
The transition from military-only rule will go on until the NLD government officially starts its term in April. The army overthrew the last democratically-elected parliament in 1962.
On Monday, among the order of business for the new parliament, will be choosing a chairman, who will then elect speakers of the two houses of parliament.
Last week Ms Suu Kyi confirmed her party will choose Win Myint as speaker of the lower house and Win Khaing Than, as the upper house speaker.