The assembly will write a new constitution for Nepal, and will formally declare the country a republic after more than two centuries of royal rule.
Elections for the 601-member assembly were first scheduled for June 20, but were postponed because the government failed to enact sufficient election laws.
The elections were then scheduled for November, but were delayed again after former Maoist fighters quit the interim government.
The impasse ended in December when the government agreed to a Maoist demand to abolish the monarchy after the election, and this was approved by parliament.
Earlier the assembly had been expected to decide the fate of the monarchy, but now it will only rubber stamp parliament's decision to turn the impoverished nation into a republic.
Maoist fighters in Nepal took up arms against the monarchy in a conflict that has caused more than 13,000 deaths since it began in 1996.