The Prime Minister will publish a bill that would only need a simple majority to succeed - not two thirds as required in previous attempts, the BBC reported on Monday.
But he would still need support from Lib Dems and the SNP for it to pass.
Johnson told MPs Parliament was "dysfunctional" and could "no longer keep this country hostage" but Labour said the Prime Minister could not be trusted.
The Commons backed the government's election motion by 299 to 70 - well short of the two-thirds majority needed under the Fixed-Term Parliaments Act.
All Conservative MPs backed the motion - but the vast majority of Labour MPs abstained, along with the SNP and DUP. All but one Lib Dem MPs voted against it.
The vote came after the PM officially accepted the EU's offer of an extension to the Brexit process to January 31.
In a letter to EU officials, Johnson said the further three-month delay - which he insists was forced upon him by Parliament - was "unwanted".
This means the UK will not now leave the EU on Thursday - October 31 - a promise Johnson had repeatedly made since he became prime minister.
Johnson said he would persist with his efforts to get an early election, telling MPs that "one way or another" the current deadlock had to be broken.
Commons leader Jacob Rees-Mogg said the government wants the House of Commons to debate all stages of a bill for a December 12 election on Tuesday.
Usually a bill is debated over the course of several days, but Rees-Mogg said the legislation would be "extremely short, simple, and limited in scope".
The bill would also have to pass through the House of Lords at a later date if it is to come into effect.
He added that the government would not be bringing back its Withdrawal Agreement Bill, required to put Johnson's Brexit deal into law.
The legislation for an election the PM is proposing for Tuesday would require a lower threshold for approval and, crucially, the Liberal Democrats and the SNP have indicated they might be prepared to support it.
( With inputs from IANS )