Kelly, who oversees Immigration and Customs Enforcement and Customs and Border Patrol, has been one of the targets of criticism for the Trump administration's hardline immigration policies.
Priebus has been under fire for weeks, seeing one White House ally after another resign or leave, culminating in the recent departure of press secretary Sean Spicer. But he clashed with Scaramucci, a Wall Street financier, and had been under siege by Trump advisers inside and outside of the White House who complained that he was ineffectual.
Amid another explosion of infighting on his White House staff, Trump is telling people he wants "a general" to take charge of the operation as chief of staff. Kelly has been a staunch supporter of Trump, during his election campaign days.
Sally Yates - acting USA attorney general, was sacked by Trump in January after she ordered Justice Department lawyers not to enforce Trump's immigration ban.
The White House has questioned the neutrality of Mr Mueller and sought to discredit him over his friendship with the sacked former Federal Bureau of Investigation chief James Comey.
Nielsen will be fulfilling a role that has been open since Katie Walsh left the White House in March after just two months on the job. His last day will be Monday, July 31, at which point Deputy Secretary Elaine Duke will become acting secretary, DHS press secretary Dave Lapan said in a statement Friday. The entire Administration loves him and no one is comparable. Assembly Majority Leader Jim Steineke echoed those comments, also tweeting that it was a "bad move by Trump".
"I'm always going to be a Trump fan", Priebus said.
"I'm doing great", Priebus said. Sanders said Priebus was loyal in his dedication to the President. But the national politicians of the party are as yet far from unified in their backing of President Trump.
"Reince Priebus has left it all out on the field, for our party and our country. I am honored to be asked to serve as the Chief of Staff to the President of the United States".
Asked by reporters if Priebus was sacked, incoming White House press secretary Sarah Huckabee Sanders said, "We all serve at the pleasure of the president".
Both Scaramucci and Priebus travelled to New York's Long Island with Trump on Friday for an event where the president highlighted efforts to crack down on the gang MS-13. "We didn't even know it". "He intuitively determined that it was time to do something different, and I think he's right".
President Trump took to his favorite social media platform to name a new Chief of Staff. Whatever his issues, Reince Priebus had spent years tugging the forelock to the many fools and knaves he had to ask for marching orders, money and personal patronage.
"They've got all these chiefs running about with or without the title of chief", said William Daley, the second chief of staff for President Barack Obama.
"I thank you for the opportunity to serve as your Secretary".
"I congratulate Secretary Kelly on his appointment, and look forward to working with him to advance our agenda", Ryan added.