"In our commentary about what had become known as Pizzagate, I made comments about Mr. Alefantis that in hindsight I regret, and for which I apologize to him. We were participating in a discussion that was being written about by scores of media outlets, in one of the most hotly contested and disputed political environments our country has ever seen," Jones said in a statement he posted to his website, Infowars.
In February, Alefantis sent Jones a letter asking for a retraction of statements made on air about him and his business. Alefantis' team considered taking legal action, which likely moved Jones to make a formal withdrawal of his claims.
On Friday -- the same day Jones released his statement -- Welch, of Salisbury, North Carolina, said during a hearing in U.S. District Court in Washington that he had agreed to plead guilty to interstate transportation of a firearm and assault with a dangerous weapon. As part of the guilty plea, prosecutors will drop a third charge, possessing a firearm during a crime of violence, which had carried a mandatory minimum prison term of five years.
He faces a sentencing hearing scheduled for June 22.
In a statement, Alefantis said he hoped those who had spread the falsehoods would be held accountable.
"I am pleased that Mr. Jones has apologized and admitted that he and his employees repeatedly spread falsehoods about me and my restaurant," Alefantis said. "I wish that he would have made this admission and apology months ago. And his apology, while welcome, does nothing to address the harm he and his company have done to me, my business, and my community."
Meanwhile, people who believed the "Pizzagate" theories that grew in conspiratorial corners of the Internet, gathered today in protest outside the White House.
On a small stage in Lafayette Park, surrounded by signs that read "We demand a criminal investigation now!" and "Fake news? Decide for yourself," organizers continued to make their baseless claims that the pizza restaurant was a front for a national pedophilia and sex trafficking ring. They also brought up conspiracy theories involving everything from the DC Metro to the television show "Shark Tank."
The "Pizzagate" scandal spread by websites like Infowars became a prime example of the potential dangers of spreading false information. The story was picked up in discussion panels on the Internet, and made it all the way to people involved with the Trump transition.
In February, after the ouster of the senior Flynn from the White House, Clinton noted the connection.
"Philippe's got his own way of saying things, but he has a point about the real consequences of fake news," she said, retweeting Philippe Reines, who tweeted, "Dear Mike Flynn & Mike Flynn Jr., What goes around COMETS around. And given your pizza obsession... https://jobs.dominos.com/dominos-careers/ … xo."
The Associated Press contributed to this report.