Joyce, a former Finance Minister who resigned from Parliament last month, said politicians should expect robust criticism but he drew the line at defamatory comments.
"The particular article that Mr Hooton wrote I believed was defamatory, took a legal case and he's decided to settle it, and that's the apology that is being made today."
It has previously been reported that Joyce was upset at Hooton's allegation that the MP only received four caucus votes in National's leadership contest, but Joyce said that was not correct.
"That wasn't one of the particular issues," he said.
Joyce has also taken a defamation case against the NBR, which is refusing to back down.
The newspaper ended its relationship with Hooton soon after the column was published. But the article remains on its website.
Publisher Todd Scott said on Twitter that Hooton had "cut a deal" without consultation with his company.
Hooton, the managing director of PR firm Exceltium, is now a columnist for the Herald.