Duggar, 27, who found fame on show 19 Kids and Counting, confessed to being a member of infidelity website Ashley Madison and cheating on his wife Anna.
It has been reported he will now check into Reformers Unanimous in Illinois to spend six months 'reading the Bible, doing manual work and praying'.
The organisations website said it would build "the relationship with Christ necessary to enjoy their freedom from the power of sin".
The Daily Mail reported the facility had no access to email or mobile phones and very limited television.
Before the scandal emerged Duggar had been a respected conservative Christian and often spoke in local media about faith issues.
The Duggar family said they were "deeply grieved" by the man's "decisions and actions".
"His wrong choices have deeply hurt his precious wife and children and have negatively affected so many others. He has also brought great insult to the values and faith we hold dear.
"For him it will be a long journey toward wholeness and recovery. We pray that in this he comes to complete repentance and sincere change."