He explained: "It was 1,000 dead actual rats which were ordered from the sanitation department of New York City and sent out from Chicago to 1,000 disc jockeys who were busy playing disco in the middle of the 70s."
"So that was basically the end of the Boomtown Rats in America."
Bob sent the packages so they would arrive at radio stations on a Monday, giving the DJs a bizarre start to their week.
Speaking during an appearance on UK TV show 'The One Show', he added: "On Monday morning there was this dump on the desk of a 1,000 DJs and it was a rat in formaldehyde, wrapped in plastic."
Meanwhile, despite having had a prolific career, Bob recently said he used to fear being homeless and destitute by the time he reached 60.
The 'Trash Glam Baby' singer began volunteering in a shelter to help those on the streets of Dublin when he was 15, and said his "greatest fear" was that he too would end up one day sleeping outside.
He said: "At 15, I volunteered at the Simon Community."
"My greatest fear was that I'd become one of the people I was working with, gathering around the big fire we had in Smithfield, taking the soup we were making."
"That was my image, at 60, sleeping on a park bench in the cold, so I had to keep running, keep running. And I can't stop."