He said the bill was "designed to overturn" the result of the 2016 Brexit referendum, in which 52 per cent voted to leave the EU.
"In the view of this government there must now be an election on Tuesday the 15th of October," Johnson said.
"I don't want an election, the public don't want an election, but this house has left no other option," he added.
Johnson, who does not have a majority in parliament, insisted he could still negotiate a new Brexit deal with Brussels in time for Britain to leave the EU on October 31.
But he said it was "completely impossible for government to function" under the terms of the new bill, which still requires approval by parliament's upper house, the Lords.
The bill enables urgent legislation requiring Johnson to ask the EU for a Brexit delay until January 31, unless parliament approves a new deal or votes in favour of a no-deal Brexit by October 19.
A vote on Johnson's call for an election is scheduled later Wednesday night.
The prime minister needs the backing of two-thirds of lawmakers for an election to go ahead, but Labour and other opposition parties said they would not support it until the legislation to prevent a no-deal Brexit becomes law.
If Johnson fails to secure backing for an election on Wednesday, he could return to his earlier plan, announced last week, to suspend parliament from mid-September until mid-October.
He once again insisted on Wednesday that he will take Britain out of the European Union on October 31 as currently scheduled, with or without a withdrawal deal with the EU.
Wednesday's parliamentary votes were made possible by an emergency motion approved Tuesday night that allowed lawmakers to set the daily agenda instead of the government.
The prime minister's party suspended 21 Conservatives who backed that effort on Tuesday, in what one member of the rebel group, former chancellor Philip Hammond, called a "mass purge."
Hammond told parliament in Wednesday's debate that preventing Britain leaving the EU without a deal was necessary because "there is no mandate for a no-deal Brexit and a no-deal Brexit will be a catastrophe."
In his first appearance at prime minister's questions since taking office in late July, Johnson said earlier Wednesday that he still aimed to negotiate a new Brexit deal before a European Council summit on October 17.
He said he remains confident that EU leaders will agree to remove a controversial "backstop" provision from Britain's EU withdrawal agreement, which is designed to guarantee an open border between Northern Ireland and the Republic of Ireland after Brexit.
But in Brussels, an EU diplomat told dpa there was "growing frustration among the EU27 that London has not yet come forward with the promised proposal on the backstop."
US Vice President Mike Pence, who is scheduled to meet Johnson in London on Thursday, said the US "stands with the United Kingdom in its decision to leave the European Union."
But he also suggested the US would prefer to see an "orderly" exit from the European Union through negotiation, according to a public pool report of his visit.
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