As noted by the TV channel, the contents of the note were not disclosed.
The President's message to his successor has become a tradition on the day of the inauguration of the new US President.
As a rule, the note is left on the table in the Oval Office so that the new head of state can read it when he first visits the office.
Earlier, Donald Trump and his wife Melania left the White House.
The outgoing Trump promised his supporters that he would return "in one form or another," and also wished the new administration good luck.
Biden's inauguration is scheduled for 12:00 (20:00 Moscow time).