Less than a week after his upset win over Democrat Hillary Clinton in Tuesday's presidential election, Trump's choice on Sunday of Priebus, the Republican National Committee chairman and friend of House of Representatives Speaker Paul Ryan, could help him repair his strained relations with members of the Republican Party establishment in Washington.
Priebus is a longtime Wisconsin political operative who was credited with marshaling party resources for Trump's White House bid.
However, Trump gave the job of strategist and senior counselor to Bannon, a fierce critic of Ryan who spearheaded Breitbart News website's shift into a forum for the "alternative right," a loose online confederation of neo-Nazis, white supremacists and anti-Semites.
The former Goldman Sachs banker over the past year led Breitbart News in a charge against the Republican Party establishment, including Priebus' friend Ryan, alienating many veteran Republicans.
The Breitbart attacks on Ryan continued on Sunday, with an article denouncing Ryan's comment on CNN that "we are not planning on erecting a deportation force."
"Speaker Ryan is now telling voters that he will not enact a central part of Trump's mandate," a Breitbart article said.
Bannon and Priebus would work "as equal partners to transform the federal government," Trump said in a statement.
Democrats were outraged by the choice of Bannon, calling him a promoter of racism and misogyny who is backed by the white supremacist group the Ku Klux Klan. Following a 1996 domestic violence charge and subsequent divorce, Bannon's then-wife, Mary Louise Piccard, testified in court that Bannon allegedly did not want their twin daughters to attend a prestigious Los Angeles school because he didn't want them to go to school with Jews.
"It is easy to see why the KKK views Trump as their champion when Trump appoints one of the foremost peddlers of White Supremacist themes and rhetoric as his top aide," Adam, Jentleson, a spokesman for Senate Democratic leader Harry Reid, said in a statement.
US Representative Adam Schiff said Bannon's selection for a top White House job was unsurprising but alarming.
"His alt-right, anti-Semitic & misogynistic views don't belong in WH," Schiff said in a Twitter post.
In morning television interviews on Monday, Priebus defended Bannon as a wise and well-educated former naval officer and said he had not encountered the sort of extremist or racist views that critics are assailing.
"He was a force for good on the campaign," Priebus said on Fox News, adding that they were in agreement on "almost everything" in terms of advising the president-elect.
Hardline Trump backers counting on the wealthy real estate developer to keep his campaign promise to "drain the swamp" of business-as-usual Washington insiders may be disappointed after he named Priebus as chief of staff, a position that serves as gatekeeper and agenda-setter for the president.
Trump said both appointees were "highly qualified leaders" who had helped him win the White House race.