Sheehan, 68, was found dead in his hotel room at the Sunset Marquis Hotel in Los Angeles, where the band are currently touring.
“We've lost a family member, we're still taking it in,” Bono said.
“He wasn't just a legend in the music business, he was a legend in our band. He is irreplaceable.”
U2 are currently halfway through their iNNOCENCE+eXPERIENCE world tour, with a string of shows still to play in California.
Sheehan's body was discovered after the first show in Hollywood.
“With profound sadness we confirm that Dennis Sheehan, U2's long-standing tour manager and dear friend to us all, has passed away overnight,” Arthur Fogel, CEO at Global Touring and chairman at Global Music Live Nation Global Touring, said.
“Our heartfelt sympathy is with his wonderful family.”Reuse content