The summit Friday comes at a contentious moment between the incoming and outgoing administrations, rooted in Russia's meddling in the US election. White House Press Secretary Josh Earnest has hammered Trump and his campaign for dismissing US intelligence showing Moscow used hacks to interfere in the US vote.
The rare gathering of White House chiefs of staff will offer Priebus a historical look at one of the most powerful jobs in Washington as he prepares to assume the post in January.
A White House official said the meeting was in line with President Barack Obama's "directive for a smooth transition to the next administration."
Chicago Mayor Rahm Emanuel -- who served as President Obama's first chief of staff -- planned to attend the meeting Friday, according to his spokesman, joining current Chief of Staff Denis McDonough. A full list of attendees for Friday's meeting was not available on Thursday night.
"When the mayor was tapped by President Obama to serve as chief of staff, (then-White House chief of staff) Josh Bolten organized a bipartisan meeting of living former chiefs of staff," said the spokesman, Adam Collins. "The mayor is happy to attend Friday's meeting as Mr. McDonough continues that tradition -- one the mayor deeply appreciated."
Emanuel met with Trump in New York last week and delivered a letter encouraging the President-elect not to deport the children of undocumented immigrants. He told reporters in the lobby of Trump Tower that it was a "very good" meeting.
Priebus was unveiled as Trump's chief of staff shortly following the election, though he shared billing on the announcement with Steve Bannon, the CEO of Breitbart who officials say will share an equal role with Priebus in the White House.
McDonough and Priebus have spoken since the announcement, and the incoming chief of staff has also consulted with other predecessors.
The 2008 meeting gathered 12 former chiefs of staff to share advice and counsel to Emanuel as he prepared to assume the office.
One of the attendees then was John Podesta, who served as chief of staff under President Bill Clinton. He was a primary victim of the Russian hacking attempt this year, and is planning to attend Friday's meeting.
Other planned attendees include former Obama chiefs of staff Jack Lew, Bill Daley, and Pete Rouse; Bush aides Bolten and Andy Card, top staffer to George H.W. Bush Samuel Skinner, Reagan chief of staff Ken Duberstein, and Jack Watson, a top aide to Jimmy Carer.