UPDATE: This report, originally scheduled for last weekend but delayed, will air this weekend, CBS News has announced.
In 45 years on the air, "60 Minutes" has never talked to a serial killer.
Cullen says he is sorry for killing 30 to 40 people with medication and knew what he was doing was wrong. Yet he says he might have continued if he hadn't been caught.
"There is no justification … the only thing I can say is that I felt overwhelmed at the time," Cullen tells Kroft.
Kroft seeks an explanation for the victims' families, and Cullen replies: "It felt like I needed to do something, and I did. And that's not an answer to anything."
Kroft interviewed Cullen last month at the New Jersey State Prison in Trenton, where the serial killer is serving 17 life sentences.
The report also features people for responsible for catching Cullen: Detective Tim Braun, Detective Danny Baldwin, Dr. Stephen Marcus and nurse Amy Ridway.
The report airs at 7 p.m. Sunday on WKMG-Channel 6.
The CBS news magazine will play portions of Cullen's confession tape. On it, he says, "I tried to kill myself throughout my life because I never really liked being who I was. I didn't feel I was worthy of anything."
Charles Graeber, who wrote "The Good Nurse" about Cullen, said the Angel of Death could have killed many more than 30 to 40 people.
Will you be watching?