The Labour leader said voters had a “once in a generation” chance to save the NHS, which was in “greater danger” than at any time in its history.
He said voters had the chance to back “real change” and an end to austerity.
But the PM warned of “economic catastrophe” and “political disaster” if Labour got into power.
Political parties are bracing themselves for a general election campaign after MPs voted for a 12 December poll.
The legislation approved by MPs on Tuesday will later begin its passage through the House of Lords, where it is not expected to be opposed.
In their final encounter in Parliament before the election, the two leaders exchanged barbs over their political values and disputed their parties’ respective records on the NHS.
The Labour leader accused the PM of running down the health service, saying cuts to funding had contributed to rising waiting times for cancer treatment and other operations.
He said a Labour government would reverse the privatization of the NHS, saying it existed to “make people better, not make the wealthy few richer”. “The choice at this election cannot be clearer,” he said.
“People have the choice to vote for real change after years of Conservative and Lib Dem cuts, privatization and tax handouts for the richest.”
Mr Johnson said he agreed voters faced a “stark choice” between a government spending “unrivalled” sums on the NHS and a Labour party that would “destroy the economy”.
Dismissing the Labour leader as an “Islingtonian protester” rather than a real leader, he said Mr Corbyn’s “flip-flopping” over Brexit would lead to more years of “toxic, tedious, torpor”.
While 2020 would be a “wonderful year” under a Tory government, he said electing Jeremy Corbyn would result in further referendums on Europe and Scottish independence.
“That is the future. Drift and dither under the Labour Party or taking the country forward to a brighter future under the Conservatives. That is the choice the country faces.”
The election comes after the EU extended the UK’s exit deadline to 31 January 2020 – although Brexit can happen earlier if a deal is agreed by MPs.
- The Early Parliamentary General Election Bill – which prompts the election – will be debated in the House of Lords on Wednesday
- If peers make any amendments to the bill, it will head back to the Commons for MPs to approve or reject the changes
- Once passed, the bill will receive Royal Assent – when the Queen formally agrees to the bill becoming law
- On Monday 4 November, MPs are due to elect a new Speaker to replace John Bercow
- Just after midnight on Wednesday 6 November, Parliament will be shut down or “dissolved” – meaning every seat in the House of Commons becomes vacant
- Five weeks later, the country will go to the polls for the first December election since 1923