The couple dated for several months before exchanging vows in the brief, quirky ceremony.
"She wanted to do the whole thing in a Cadillac. That was her thing," the celebrity magazine quoted a witness as saying. "She cried during the vows and had to wipe her eyes."
The event took place on the "Nothing Compares 2 U" singer's 45th birthday.
People.com said employees of the chapel sang "Happy Birthday" to the bride after the wedding.
O'Connor has been divorced three times.
The Hollywood Reporter described Herridge as a therapist who answered O'Connor's online appeal for a mate.