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A message on the official festival website confirmed that the band will headline the Pyramid Stage on Friday night.
Organiser Michael Eavis said: "The 26-year-old rumour has finally come true. At last, the biggest band in the world are going to play the best festival in the world!
"Nothing could be better for our 40th anniversary party. And there are even more surprises in the pipeline."
A source told The Sun: "In fact Eavis has been asking them for a while now and really stepped up the effort this year. This could be an iconic moment."
U2 will play shows in Edmonton, Canada and Minneapolis, Minnesota either side of their Glastonbury appearance.
Other bands tipped to play next year's anniversary event include The Rolling Stones, Coldplay, David Bowie and Muse.
Glastonbury 2010 takes place from June 23 to 27, 2010 at Worthy Farm, Pilton, Somerset.
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