Also billed as headliners for the two festivals, both to be held on August Bank Holiday weekend, are My Chemical Romance, a reformed Pulp and The Strokes.
"We're honoured to be sharing headlining with them," said My Chemical Romance's Gerard Way.
"The Strokes are one of our all time favourite bands."
Muse headline the last day at Reading's Little John's Farm and the first at Bramham Park in Leeds.
Other acts confirmed for both Leeds and reading include Beady Eye, Pete Doherty, Elbow, Interpol, Jane's Addiction, Jimmy Eat World, Madness, Noah & The Whale and The Streets.