The Los Angeles County Coroner said Sheehan, 68, died Wednesday morning of natural causes at a hotel in West Hollywood.
Sheehan's death came hours after the first concert Tuesday night of a five-show run at The Forum in Los Angeles, part of a 20-city tour.
"We've lost a family member, we're still taking it in," said lead singer Bono on the group's website.
"He wasn't just a legend in the music business, he was a legend in our band. He is irreplaceable."
Sheehan worked for many big names in the music industry, and was singer Robert Plant's assistant on Led Zeppelin's 1977 US tour before joining U2 on the road.
The 22-time Grammy winners, known for hits like "Sunday Bloody Sunday" and "Beautiful Day," has embarked on almost 20 tours since forming in 1976.