He also accused Mr Priebus of being behind the flow of damaging leaks about the White House and said he was going to ask the FBI to investigate him.
Kelly, a retired Marine general, has been serving as Homeland Security secretary. "He has been a true star of my Administration".
As for Kelly, until now, he was US Secretary of Homeland Security, nominated by Trump on December 2, 2016.
As Secretary of Homeland Security, Kelly has played a key role in the border security of the Trump administration.
Later in a statement, the White House Press Secretary Sarah Sanders said Kelly would begin his new responsibility Monday morning. "He is respected by everyone, especially the people at the Department of Homeland Security". One of those sources says Trump's kin urged the President to finally execute a long-pondered shake-up. He went on to mock Trump's senior advisor Steve Bannon, saying "I'm not Steve Bannon, I'm not trying to suck my own c**k".
Vice President Mike Pence tweeted that he was "g$3 rateful to Reince for his friendship and service to America", adding that Priebus has "been a huge part of our success!"
"I think bringing in a fresh face, I think bringing in fresh people, is a good thing", he said. Priebus has had a diminished profile in the White House for weeks, and the president hasn't exactly expressed support for him.
"I will continue to serve as a strong supporter of the president's agenda and policies".
Privately, even Mr Priebus's critics wondered how Mr Kelly would surmount the same challenges - controlling a freewheeling president who often circumvents paid staff members by seeking counsel from a roster of outside advisers.
Incoming White House chief of staff John Kelly will likely keep a top aide as he settles into his new role.
"I'm sure this is the first chief of staff removed in the way he was removed", Card, who served under former President George W. Bush, told Ari Melber Friday on MSNBC.
Scaramucci clearly has no qualms over bad-mouthing Priebus-calling him a "paranoid schizophrenic, a paranoiac" during the New Yorker interview.
In fact, he chatted with Priebus repeatedly during the flight. "We've gotten to know each other very well".
The president made the announcement on Twitter.
Scaramucci reiterated that Priebus would resign soon, and he noted that he told Trump that he expected Priebus to launch a campaign against him.
Before accepting the position, Scaramucci served as the vice president and chief strategy officer at the Export-Import Bank, a position he held since June 19.