Aregood has been editor of the Daily News' editorial and opinion pages since 1975, and will have the same responsibility at the Newark paper, starting Feb. 27.
He said he was looking forward to new opportunities in Newark, including building an editorial- page staff there.
Aregood, 52, joined the Daily News as a reporter in 1966. His other jobs on the paper included features editor, news editor and deputy sports editor.
Stalberg said he was saddened by Aregood's departure.
"He is a unique talent who brought attention and glory to this newspaper over a long period of time," Stalberg said in a memo to the staff. "He has a wild mix of traits and skills, but one of them was a deep concern - and ability to develop - the people who worked with him. In this, he will remain a model for the rest of us who try to be editors.
"Beyond that, Aregood was a wise adviser and friend to me over a long period of time. I think Rich would agree that our friendship has been bruised over the last several weeks, but remains fundamentally strong."
"My relation with Zack over the long term has been very good," he said.
One area of dispute, according to both, was Stalberg's decision to cut back the editorial pages' staffing and newspaper space in the wake of rising costs.
Said Aregood: "I don't feel either the space or the manpower would have been devoted to the editorial pages to do it the way I would like to do it."
They also differed on the "mission" of the editorial pages, said Stalberg.
"I'm not looking for a different ideological tilt on the editorial pages," he said yesterday. The disagreement with Aregood, he said, was over how the paper's viewpoint should be expressed.
Aregood said he didn't want to comment on that issue.
He said he was sad to leave the paper.
"It's been a long time," he said. "The Daily News gave me the opportunity to write. I came to the Daily News when I was 23. I grew up at the Daily News."