The Friday slot makes Muse the first band to have headlined every night of the festival – they played on Saturday night in 2010, and Sunday in 2004.
Muse posted a video on Friday titled “Playing a little show at home…” showing clips from their previous Glastonbury performances.
The band won a Grammy for best rock album earlier this month.
Their seventh studio album, Drones, was released last June.
Coldplay revealed last week they would headline the Pyramid Stage on Sunday.
The Saturday headliners are yet to be announced – but Jeff Lynne’s ELO have been confirmed for the Sunday teatime slot.
The 2016 Glastonbury Festival runs from June 23 to 26.
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