Mr Klain has served as a top aide to Mr Biden since the 1980s in the Senate and later when he was vice-president.
The ultimate Washington insider, Mr Klain was also a senior White House aide to Barack Obama and chief of staff to Vice-President Al Gore.
He was played by actor Kevin Spacey in the movie Recount, about the presidential election of 2000.
The White House chief of staff - who manages the president's daily schedule and is often described as his gatekeeper - is a political appointee that does not require confirmation by the Senate.
