The announcement had been expected for the past few days, with campaign manager Kellyanne Conway telling media earlier in the day that both would have major roles in the new administration.
Priebus has deep ties to Republican leadership in the House and Senate, but little governing experience. Bannon is the chair of the right-wing Breitbart News organization.
"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,” Trump's team said in a statement.
"I am thrilled to have my very successful team continue with me in leading our country. 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."
Priebus and Bannon both thanked Trump for the honor.
"I am very grateful to the President-elect for this opportunity to serve him and this nation as we work to create an economy that works for everyone, secure our borders, repeal and replace Obamacare and destroy radical Islamic terrorism. He will be a great President for all Americans," Priebus said.
"We had a very successful partnership on the campaign, one that led to victory," Bannon said. "We will have that same partnership in working to help President-elect Trump achieve his agenda."