The reality show "will no longer appear on the air," the network told the Associated Press in a statement Thursday.
TLC pulled the plug on 19 Kids following public pressure that erupted when a resurfaced police report from 2006 revealed that Josh had been investigated for child molestation of six people when he was a teen.
His sisters Jill Dillard, 24, and Jessa Seewald, 22, later came forward as two of the six victims, insisting they had already "moved on" and forgiven their brother when the news broke.
The Duggars released a lengthy statement Thursday about the decision, thanking their TV crew, fans and God.
"With God's grace and help, Josh, our daughters and our entire family overcame a terrible situation, found healing and a way forward. We are so pleased with the wonderful adults they have all become," they said. "It is our prayer that the painful situation our family went through many years ago can point people toward faith in God and help others who also have lived through similar dark situations to find help, hope and healing, as well."
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The family also suggested that the controversy will be covered in an "upcoming special documentary" on TLC.
On the day that the Duggars responded to the reports of alleged molestation in statements to PEOPLE, the network aired a 19 Kids marathon. The following day, TLC decided to pull reruns of the show from its schedule, announcing, "We are deeply saddened and troubled by this heartbreaking situation, and our thoughts and prayers are with the family and victims at this difficult time."
The Duggar family chalked the accusations up to "teenage mistakes" in their respective statements.
"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," Josh, 27, said in his statement to PEOPLE released May 21.
"I confessed this to my parents who took several steps to help me address the situation," Josh continued. "We spoke with the authorities where I confessed my wrongdoing, and my parents arranged for me and those affected by my actions to receive counseling."
However, as the reports reveal, Josh's three-month stay in a treatment program at the age of 14 in Little Rock, Arkansas, was not actually run by a certified counselor but by a family friend of the Duggars who was in the home-remodeling business. Josh was only put through "hard physical work."
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In their own joint statement, Michelle, 48, and Jim Bob, 49, said that the incidents of alleged molestation – which were reported to have occurred in 2002 and 2003 – brought the family closer together. "Even though we would never choose to go through something so terrible, each one of our family members drew closer to God. We pray that as people watch our lives they see that we are not a perfect family. We have challenges and struggles every day."
As a source close to the Duggars previously told PEOPLE, Michelle and Jim Bob were "devastated" over the leak. "They know that they did the best they could, but it doesn't mean they're not filled with regret."
That said, the future of 19 Kids – an enterprise on which they've built a massively profitable empire including book deals and speaking engagements – was never their concern once their secrets became public knowledge. Added the insider: "Right now they're just focused on their faith – and each other."