His cabinet resigned on Thursday to make way for the new administration and Mr Bhattarai will step down by the end of the month, aides say.
Parties have vowed to meet the deadline, having missed previous ones.
The new constitution is a key part of a peace process launched in 2006 after Maoist rebels ended a 10-year revolt.
Mr Bhattarai, a senior Maoist leader, is expected to form the coalition government over the weekend, his office said.
The Maoists won most seats in elections in 2008 but fell short of an overall majority in the Constituent Assembly.
It was given two years to write a new constitution but that deadline has been extended as negotiations have faltered.
Nepal’s Supreme Court has set what it says is a final deadline of 27 May for parties to reach agreement.