The 67-year-old now tells People that the incidents took place between 1973 and 1994 with three different victims, adding, "I have not had an impulse to act out in any such way" in the last 20 years.
Collins explained in the statement, "Forty years ago, I did something terribly wrong that I deeply regret. I have been working to atone for it ever since. I've decided to address these issues publicly because two months ago, various news organizations published a recording made by my then-wife, Faye Grant, during a confidential marriage therapy session in January, 2012. This session was recorded without the therapist's or my knowledge or consent."
He continued, "On the recording, I described events that took place 20, 32, and 40 years ago. The publication of the recording has resulted in assumptions and innuendos about what I did that go far beyond what actually occurred. As difficult as this is, I want people to know the truth."
Collins, who will sit down with Yahoo Global News Anchor Katie Couric on Friday, also addressed why he hasn't apologized to the women.
"I did have an opportunity to do so with one of the women, 15 years later. I apologized and she was extraordinarily gracious," he said. "But after I learned in the course of my treatment that my being direct about such matters could actually make things worse for them by opening old wounds, I have not approached the other two women, one of whom is now in her 50s and the other in her 30s."
For the full statement, pick up the latest issue of People, on newsstands Friday.