In his keynote speech to Labour's annual conference in Brighton, Mr Corbyn declared that Labour was ready for government and urged Theresa May to call another snap election to put him into Downing Street.
Buoyed by loud chants of "Oh Jeremy Corbyn" which delayed the start of his address, the Labour leader said that a "new consensus" had emerged a decade after the financial crash of 2008, with voters ready for "something different and better".
The Grenfell Tower fire which killed 80 in west London in June was the symbol of a "degraded" political system which had dominated Britain for a generation, and which Labour was now ready to sweep away, he said.
To fervent applause, he promised to end the public sector pay cap, close the gender pay gap, tackle inequality, renationalise utilities, rebuild the NHS and invest in the economy.
After a four-day conference characterised by optimism and largely free of the infighting seen in his first two years as leader, Mr Corbyn said it was clear that Labour had achieved unity and "left our own divisions behind".
He told activists that Labour now needed to show that it had the "credible and effective" plans and the competence needed to deliver "socialism for the 21st century, for the many, not the few".
And in a message to those who backed Labour on June 8, he said: "We offered an antidote to apathy and despair. L et everyone understand - we will not let you down.
"Because we listen to you, because we believe in you. Labour can and will deliver a Britain for the many, not just the few."
Denouncing the Government's "bungling" of Brexit negotiations, Mr Corbyn claimed Theresa May and her ministers were "hanging on by their fingertips", and mocked the Prime Minister's "strong and stable" election slogan.
"This is a deeply divided Government with no purpose beyond clinging to power," he said. "It's Labour that's now setting the agenda."
And recalling Mrs May's decision to call a snap election during a hiking trip in Snowdonia, he challenged the Prime Minister: "Take another walking holiday and make another impetuous decision. The Labour campaign machine is primed and ready to roll."
He told activists: " Conference, it is often said that elections can only be won from the centre ground.
"And in a way that's not wrong - so long as it's clear that the political centre of gravity isn't fixed or unmovable, nor is it where the establishment pundits like to think it is. It shifts as people's expectations and experiences change and political space is opened up.
"Today's centre ground is certainly not where it was 20 or 30 years ago.
"A new consensus is emerging from the great economic crash and the years of austerity, when people started to find political voice for their hopes for something different and better."
The Labour leader said that "2017 may be the year when politics finally caught up with the crash of 2008 - because we offered people a clear choice".
He added: "We need to build a still broader consensus around the priorities we set in the election, making the case for both compassion and collective aspiration.
"This is the real centre of gravity of British politics. We are now the political mainstream.
"Our manifesto and our policies are popular because that is what most people in our country actually want, not what they're told they should want."
The audience in the packed auditorium rose for an extended standing ovation following Mr Corbyn's 73-minute speech.
The leader himself applauded the delegates as John Lennon's Power To The People rang out around the hall. But he swiftly removed a red and yellow garland which was placed around his neck as photographers gathered.
A choir led the conference in its traditional rendition of The Red Flag, followed by Jerusalem.