"While espousing faith and family values, I have been unfaithful to my wife," Duggar, 27, a former campaigner for family values who appeared on the TLC show "19 Kids and Counting," said in a statement posted on his family's website.
"The last few years, while publicly stating I was fighting against immorality in our country I was hiding my own personal failures," he added, calling himself the "biggest hypocrite ever."
The Discovery Communications-owned network last month canceled "19 Kids," after disclosures in May that Duggar had sexually abused four of his sisters when he was a teenager, one of whom was under 10 years old at the time.
Related Reading
More Ashley Madison website data leaked online
Duggar apologized in a statement, saying he "acted inexcusably," and resigned from his job at Christian lobbying group Family Research Council.
In an earlier version of Duggar's statement posted on the family's website and reported by People magazine and Buzzfeed, he said "I have secretly over the last several years been viewing pornography on the internet and this became a secret addiction and I became unfaithful to my wife."
The reference to pornography was removed in an updated version of the statement.
Duggar's parents, conservative Christians Jim Bob and Michelle Duggar, said on Thursday they were dismayed over the Ashley Madison reports concerning their son.
"When we learned of this late last night our hearts were broken," they said in a statement.
Hackers this week dumped a batch of data stolen from the Ashley Madison website detailing millions of members. The site's tagline is "Life is short. Have an affair."
Duggar is so far the highest-profile person found among the site's clientele.
A link to the statement was posted on the Duggar family's Facebook page but deleted after a barrage of comments from fans criticizing Josh Duggar for his actions. On Twitter, Duggar became a trending topic as users expressed their disapproval.
A TLC representative declined to comment on Thursday, but said the network is still scheduled to release "Breaking The Silence" on August 30, a documentary on child sex abuse featuring Duggar's sisters Jill and Jessa, who publicly forgave him for molesting them in the past.
Duggar and his wife, Anna, were married in 2008 and have four children.
