"Steve and Reince are highly qualified leaders who worked well together on our campaign and led us to a historic victory. Now I will have them both with me in the White House as we work to make America great again," Trump said in the release.
It's an unusual arrangement that could create two power centers in the new White House, one around the Republican establishment and one connected to the far right and more controversial wing of conservatism. The campaign statement, which listed Bannon's role first, referred to the two men as "equal partners."
"Bannon and Priebus will continue the effective leadership team they formed during the campaign, working as equal partners to transform the federal government, making it much more efficient, effective and productive," it said.
The dynamic will continue the structure of the two men's roles in the campaign, with Priebus and Bannon working as partners, but with very different Trump constituencies to manage. Both Priebus and Bannon were highly involved with working out the arrangement, a source familiar with the decision said.
Bannon represents bare-knuckle style politics seen as appealing
to Trump's most inflammatory instincts, and his initial hiring prompted a raft of criticism from Democrats accusing Trump of embracing the "alt right," an ideology closely associated with white nationalism, anti-Semitism and misogyny.
Priebus should be a reassuring presence to establishment Republicans still uncertain about what a Trump White House will look like. The pick signals that Trump may look to build bridges in Washington and keep continuity with longtime Republican agendas, as opposed to make waves from the beginning.
Priebus is among the longest serving chairmen of the Republican Party, and has generally been popular amid different factions within the party. He is largely credited with building the ground game that elected Trump and with helping to unite his party after a divisive primary that resulted in many Republicans shunning Trump's nomination.
Trump's choice for chief of staff was believed to come down to Priebus and Bannon. In a repeat of the tumultuous process that led Trump to tap Indiana Gov. Mike Pence of Indiana as his running-mate, GOP officials pressed the President-elect to go with Priebus for the chief of staff job.
House Speaker Paul Ryan and Senate Majority Leader Mitch McConnell urged Trump on Thursday to pick Priebus, a source told CNN on Friday. Trump's son-in-law and top adviser, Jared Kushner, has also said privately he is supportive of that decision.
After the announcement, a spokesman for Ryan said the speaker was pleased by the decision.
"The speaker is very happy for his friend and ready to get to work," said Doug Andres, his spokesman.
Priebus has served as a negotiator between the party and Trump. When Ryan did not initially endorse Trump, Priebus organized meetings and helped diffuse tension between the two when Ryan criticized Trump and Trump hit back.
Sources say Priebus and Trump have grown very close over the course of the campaign. Priebus had a leadership role in Trump's debate prep and traveled with him in the latter days of the campaign. Many of the RNC's top operatives were installed in Trump Tower to work closely with the campaign.
During the campaign, Trump often said he would look to politicians to help him govern, including his selection of Pence -- another Ryan friend and ally -- as vice president. But he also ran a campaign as an outsider, saying he would "drain the swamp" of Washington.
Priebus earned Trump's trust in the final months of the campaign, as he steered the RNC's resources behind Trump's candidacy despite Republican officials urging Priebus to abandon Trump and instead help down-ballot candidates.
As Trump's candidacy was engulfed in the controversy stemming from a 2005 tape in which he boasted about being able to grope and kiss women without their consent, and as sexual assault allegations surfaced the next week, Priebus stood fast behind Trump and worked to salvage his campaign.
Trump's debate over the selection demonstrated how he was once again being pulled between a more pragmatic selection with a pick who will enable his outsider persona and bellicose instincts.
On Sunday night the Bannon appointment drew scorn from the office of Senate Minority Leader Harry Reid.
"President-elect Trump's choice of Steve Bannon as his top aide signals that white supremacists will be represented at the highest levels in Trump's White House," said Adam Jentleson, a spokesman for the Nevada Democrat, who is retiring from Congress.
And Jonathan Greenblatt, CEO and national director of the Anti-Defamation League, tweeted, "We at @ADL_National oppose the appt of Steve Bannon to sr role at @WhiteHouse bc he & his alt-right are so hostile to core American values".
But Trump ran an outsider campaign and Bannon's hiring signals an intention to keep the insurgent sentiment that propelled his campaign close.
Bannon is a former Navy officer and Goldman Sachs investment banker and has been an executive in the right-wing media for years. His website Briebart News, which Bannon has been associated with since its start in 2007, has been vehemently pro-Trump throughout his presidential campaign, and is also known for pushing nationalist policy positions, as well as conspiracy theories, and has been criticized as being racist, sexist and anti-Semitic.
Bannon's wife has also accused Bannon himself in court documents of making anti-Semitic comments
He joined Trump's campaign in August alongside new campaign manager Kellyanne Conway, after Paul Manafort was fired as campaign manager.
While pundits worried that Bannon's hiring would hasten Trump going way off-message, he had some of his most disciplined weeks of his campaign under Bannon and Conway's leadership, though it was almost derailed by a hot mic video that caught Trump bragging of sexually violent and aggressive behavior toward women.
A potential White House role for Conway is a possibility. A Trump source says the President-elect has made clear to Conway that he wants her to work in the new administration, but she has not decided whether to do so for several reasons. That includes being mother to four young children.
CNN is told Conway is more likely to stay outside the government and follow the template of President Barack Obama's 2008 campaign strategist David Plouffe, who opted not to go in the White House.
Conway may follow that model and help the Trump administration by organizing conservative groups and pushing Trump policies and legislation from the outside.
Given Conway's exposure through the Trump campaign, she is also poised to make a lot of money working outside of government.
This story has been updated.