Speaking to NME, the singer and guitarist explained that the thought of being second headliner behind Coldplay is "mind-blowing".
"It's, like, 20 years this month that the band formed, so to be celebrating here is pretty special really," said the frontman. "Playing second headliner on the Pyramid Stage is something I never thought I'd do. It's mind-blowing – it's one of those things you can't actually take in."
Garvey also had kind words for the Glastonbury organisers, and praised the distinct festival atmosphere.
The star added: "There's something about the land and the sky round here - it's pretty trippy really. I'm from the north, so there are all these hills on the horizon and there isn't in this part of the world...
"There's more sky, and if that sounds pretty hippy, it's because I am [a hippy]. You can understand why they believed in magic and stuff like that 'round here, because there's just something vibrant about it."
Digital Spy is bringing you news from Glastonbury festival 2011 all weekend - view our guide to the festival and click here to stay abreast of our full coverage.
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Watch Elbow perform 'Open Arms' at Glastonbury below: