The former Dragons captain, who will lead Wales out against Queensland Reds on Friday, was named among a group of people who damaged a woman’s home in May 2021.
Hill, who was playing for Cardiff at the time, was not charged by police and apologised at the time through a representative.
His replacement appearance in the first Test against Australia on July 6 ended more than three years out of international rugby and he has now been chosen to captain his country by Wales head coach Warren Gatland.
“That incident happened three years ago. Do I regret it? Yes, of course I do,” said the 32-year-old from Maesycoed.
“I made a mistake and I regret it. There will always be a negative reaction to mistakes that someone has made in the past.
“I have been honest and open here. The matter was addressed by the club and the authorities three years ago.
“It was a mistake. I hold my hand up high and regret what happened.”
Gatland added: “We had a chat about what happened in the past and we spoke honestly about it.
“Cory told me that he made a mistake three years ago and that he regrets what happened. Young people make mistakes.
“For me, it’s about putting that aside and picking someone with that experience and knowledge of rugby who has that respect from the rest of the players in the team.
“I have been clear that people make mistakes in life and take some decisions or actions that they wish did not occur.
“We sat down and had an honest conversation about some things. Cory was very open with me about it. I’m not looking back, but looking forward.”
Hill was co-captain on Wales’ 2018 summer tour against South Africa and Argentina and adds experience to the green team in Brisbane.
The lock has been playing in Japan since leaving Cardiff in 2021, currently with Secom Rugguts in the fourth tier.
“The first two years in Japan, I played for the Canon Eagles with a couple of world champions and also some Super Rugby players,” Hill said.
“It was a huge learning experience as a player, going out there and the intensity being high and I enjoyed it.
“I really enjoyed my time in Japan and had some fantastic experiences, and I’ll probably bring some of them back with me.
“I’ll be there for another year after we get promoted, but it’s up to us to have conversations moving forward.”
