Paul Kerr subjected Julie Fagan and her husband John to an 11-month campaign of online abuse between January and November 2018, Lewes Crown Court heard.
The 56-year-old said said he would “drag Julie Fagan by her hair” to a police station and told officers via email that he would murder her husband John.
He also posted a series of sexually abusive messages on Facebook about them and falsely accused John Fagan of raping a nine-year-old boy, the jury was told.
He had now been found guilty of three counts of pursuing a course of conduct that amounted to stalking.
Ms Fagan testified that she was "quite mortified" when Kerr threatened to rape her.
"I thought he was not only going to physically harm us, I thought he was going to sexually assault me as well,” she said.
It also emerged at trial that Kerr had stalked his ex-girlfriend Elizabeth Vanthof between April and November 2018, contacting her at home and at the French university where she worked.
Speaking tearfully after the verdict was given, Ms Fagan said the episode had been horrific, but she was still a fan of Simple Minds and had already booked tickets for the band’s upcoming world tour.
“I am just so relieved, it is the end of a horrible nightmare,” she said. “He has lied all the way through. I felt sick to my stomach."
Kerr will be sentenced on 6 January following the conclusion of a psychiatric assessment.