Corbyn pledged his support to refugees, young people and the environment, and took a swipe at USA president Donald Trump during his speech.
The chant was sung by thousands of festival goers queuing to get into the site on Wednesday morning.
Referring to the election he said: "The commentariat got it wrong, the elites got it wrong".
Corbyn tolf the crowd: "I want to say thank you to Michael for lending us his farm, for giving the space all those years ago, for people to come here and enjoy music, enjoy good company and enjoy inspiring thought".
Mr Corbyn, who had not attended the festival before, introduced U.S. hip hop duo Run The Jewels before his Left Field tent speech.
"Politics is about the lives of all of us", he told the crowds, "and the wonderful campaign that I was involved in. brought a lot of people back into politics because they believed there was something on offer for them".
He explained that the five-day festival was about "coming together" and symbolised the importance of the environment and peace.
Mr Eavis told the festival's on-site newspaper: 'Millions of young people, Glastonbury people, voted for him.
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They are under the care of other family members. "I could have taken her down", Lyles' sister, Monika Williams, told Q13 News . She tells them she left her door unlocked while she went to the store and that while she was out her Xbox was stolen.
They did so, he said, "because they were fed up with being told they don't matter and that their generation was going to pay more to get less in education, housing, health, pensions and everything else".
"I think more politicians should do things like this", said Claire Herbert, 32, from Llanelli, South Wales.
"I've heard people chanting Jeremy Corbyn around the whole site and I'm pretty happy about that as well".
The Islington North MP also went on the attack on the time that has elapsed so far as the Conservatives try to broker a deal that will see it supported by the DUP. "Just shut the door on your way out".
The Labour leader was called on stage by festival founder Michael Eavis to loud cheers after earlier being mobbed for selfies by thrilled young fans.
He also praised the Somerset festival's impact on society.
And shadow chancellor John McDonnell is due to take part in a debate at the festival today- with an awkward encounter on the cards if the Labour rivals cross paths.
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