Mr Eavis told the festival's on-site newspaper: 'Millions of young people, Glastonbury people, voted for him.
"We're demanding something very different in our society and our lives", Corbyn said.
Corbyn was on the main stage at Glastonbury for about ten minutes before American hip hop group Run the Jewels performed.
During the set, Thom Yorke stopped to thank festival organisers Michael and Emily Eavis, and share his thoughts on the festival.
The last day of 2017's festival will also host Haim, Rag "n" Bone man and Emeli Sande, along with Goldfrapp, Kano, Kiefer Sutherland and Scouting For Girls.
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"Rise like lions after slumber, in unvanquishable number, shake your chains to earth like dew, which in sleep had fallen on you - ye are many, they are few".
Welcomed on stage by festival founder Michael Eavis, Corbyn made a dig at President Trump, pointing out a poster reading "Build Bridges, Not Walls". Soccer fans in the United Kingdom have been using the not wholly complex compositional framework ("Oh + five-syllable name") for years but this seems to be have been the first time Jeremy Corbyn's name was used.
The Labour leader included the policy to back renewal of Trident in his election manifesto in recognition of the fact that it is the party's policy to keep the nuclear deterrent.
He said the U.S. president is determined to add to existing global problems and accused British Prime Minister Theresa May of pandering to him. "Shut the door on the way out". The late and much loved MP Tony Benn, a friend and mentor to Corbyn, was a regular and popular speaker at Glastonbury.
The shadow chancellor will be part of a panel discussing whether democracy is broken at the tent on Sunday.