Crowds have been chanting the Labour leader's name since arriving at the site in Pilton, Somerset, and he received a rapturous response.
Trade Union worker Hazel Nolan, 30, from Ireland, was working at the music festival's Solstice bar when Mr Corbyn surprised them with a visit.
The Labour leader ended his speech shouting: "Rise, like lions after slumber in unvanquishable number!".
The poem is seen as one of the first modern statements of the principle of nonviolent resistance.
Chris Glackin from Surrey, who was eight when the album was released, was looking forward to the gig.
A volunteer was who was served a beer by Labour leader Jeremy Corbyn at Glastonbury said it is the "best pint she's ever had". The late and much loved MP Tony Benn, a friend and mentor to Corbyn, was a regular and popular speaker at Glastonbury.
"The elites got it wrong", he said.
Building a wall on the US-Mexico border to stop the influx of refugees and undocumented migrants coming from Central and Latin America was a hallmark of Trump's presidential campaign.
In a wide-ranging speech covering environmental issues as well as racism, Corbyn also spoke about the recent general election, saying he was proud of his party's campaign, which he said brought "a lot of people back into politics".
"Millions of young people - Glastonbury people - voted for him", Mr Eavis told the festival's on-site newspaper.
Michael Vale, 28, from London, said: "I'm not sure they'd get Theresa to do this".
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".
Passengers record terrifying shaking on Air Asia flight
Water Police said marine emergency services north of Perth were put on standby to prepare for a possible water landing. Earlier, AFP quoted one of the passengers as saying the plane was " shaking like a washing machine".