The Labour leader told his party’s conference Britain had moved to the left since the 2008 financial crash which has left them “on the threshold of power”.
And the left-wing politician claimed a “new consensus” had emerged in the past decade which has meant Labour is now the party of “mainstream” voters.
Despite his party losing the last three elections, Jeremy Corbyn said the fact Labour gained 30 seats in June’s snap election proved his socialist agenda was popular.
Mr Corbyn, said: “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. 2017 may be the year when politics finally caught up with the crash of 2008 – because we offered people a clear choice.
“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.”
The Grenfell Tower fire which killed 80 people 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 Labour had achieved unity and “left our own divisions behind”.
He told activists Labour now needed to show 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. Let 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.
He said: ”This is a deeply divided Government with no purpose beyond clinging to power.
“It’s Labour that’s now setting the agenda.”