Kelly, a retired Marine general, has been serving as Homeland Security secretary.
Kelly, a retired four-star Marine general , has been serving as Homeland Security secretary.
Priebus, 45, became a target of Trump's ire shortly into his term as White House chief of staff.
Trump has consistently applied pressure on Priebus and reportedly given him various deadlines to get a tumultuous White House in order.
Reuters, citing a senior White House official, reported Friday that Trump told Priebus two weeks ago that he would replace him as chief of staff. The Wall Street Journal, likewise, said Priebus told the newspaper in a text message that he "resigned privately" Thursday.
After the announcement Friday, the president offered kind words about Priebus while delivering praise for Kelly.
"Reince is a good man. John Kelly will do a fantastic job. General Kelly has been a star, done an incredible job thus far, respected by everybody," Trump told reporters who had traveled with him Friday on Air Force One. "He's a great great American. Reince is a good man."
Priebus released a statement later Friday:
It has been one of the greatest honors of my life to serve this President and our country. I want to thank the President for giving me this very special opportunity. I will continue to serve as a strong supporter of the President's agenda and policies. I can't think of a better person than General John Kelly to succeed me and I wish him God's blessings and great success.
Priebus had been under fresh scrutiny recently when Trump brought on financier Anthony Scaramucci as communications director. Former press secretary Sean Spicer, one of Priebus' allies in the White House, left after Scaramucci's hiring.
Scaramucci created a White House spectacle Thursday following his Wednesday night tweet accusing someone of leaking a financial disclosure document that is publicly available. Scaramucci tagged Priebus in the tweet, but he later denied that he was identifying Priebus as the source.
He told CNN on Thursday that "if Reince wants to explain he's not a leaker, do that." Scaramucci compared himself and Priebus to the Biblical brothers Cain and Abel. Cain killed Abel.
On Thursday, press secretary Sarah Huckabee Sanders said, "I don't know if [Trump] has an opinion on what they should do between the two of them."
"I think the president as always enjoys healthy competition and conversation, and he sees that as such," she said.
Priebus led the Republican National Committee before coming to the White House. He had held that job since 2011.
After serving at the RNC and leading the Wisconsin Republican Party, Priebus had ties to the so-called establishment branch of the Republican Party embodied by leaders such as House Speaker Paul Ryan. That put him at odds with top Trump advisor Steve Bannon, a firebrand who helped to inspire some of the protectionism and harsh anti-immigrant rhetoric that has marked Trump's candidacy and now presidency.
Kelly, meanwhile, said he is "honored to be asked to serve as the chief of staff" to the president. He is expected to start his new job Monday.
Kelly takes on the key White House role after six months in the top spot at Homeland Security, a department that was created in the aftermath of the Sept. 11, 2001, terrorist attacks on New York and Washington, D.C. The Senate voted in January to confirm Kelly by an 88 to 11 vote. He served in the Marine Corps for 45 years, ending his career as commander of the U.S. Southern Command.
--CNBC's Mike Calia and Michael Sheetz contributed to this story.