It was Bannon - Trump's former senior strategist, fired by the U.S. president in August - who helped give Wolff access to the White House to carry out research for his bombshell book. In a statement, Bannon said that he is "proud of what the Breitbart team has accomplished in so short a period of time in building out a world-class news platform".
Bannon's exit from the right-wing website he had helped build since 2012 comes days after the publication of a book in which he is referenced as questioning President Donald Trump's mental stability.
Mr Bannon still stands by the remarks, but claims they were directed at then-campaign chairman Paul Manafort and not Donald Trump Jnr, whom he calls a "patriot and a good man".
Trump has said he never authorized any access to the White House, called Wolff's book "a Fake Book" and tweeting last week that he "actually turned [Wolff] down many times". Trump has blasted the book as inaccurate.More news: Transparency shines with Trump's immigration meet, Fusion GPS transcript release
In another quote from the book attributed to Bannon, he predicted authorities would get Don Jr.
"My family and I have not communicated with Steve Bannon in many months and have provided no financial support to his political agenda, nor do we support his recent actions and statements", Mercer said.
Conservative media outlet Breitbart News on Tuesday announced that Steve Bannon is stepping down as Breitbart's executive chairman.
However, Bannon didn't respond until Sunday when he tried to walk back some of the comments without officially apologizing.