According to police report, Duggar, 14 at that time, sexually molested five young girls.
Parents Jim Bob and Michelle reported him to police but no charges were filed, said The Hollywood Reporter.
Duggar, now 27-year-old with three kids, responded to the allegations through a statement on Duggar Family's official Facebook page.
"Twelve years ago, as a young teenager, I acted inexcusably for which I am extremely sorry and deeply regret. I hurt others, including my family and close friends.
Duggar announced his resignation from Family Reserve Council, an organisation dedicated to preserving family values in America.
His wife, who is expecting their fourth child, also released a statement, admitting he confessed about his past before their engagement.