Annie Tomasini, Deputy chief of staff, and Anthony Bernal, the senior adviser to First Lady Jill Biden, are also said to have been present for the discussions.
Anita Dunn, a senior adviser to the President, told shocked staff that the “decision came down late”.
She added that the decision had been taken by an extremely small group of people and appeared to imply that she had not been made aware beforehand.
Ms Dunn was one of several advisers who found out about the move exactly one minute before the statement went public, according to the New York Times.
Some White House staff are said to have been shocked and tearful at the decision, while others were relieved following weeks of pressure on the US President.
Kamala Harris, chief of staff Jeffrey Zients and campaign chair Jen O’Malley Dillon were informed earlier on Sunday.
A senior administration official said Mr Biden decided to step down after failing to shift the attention from his dire debate performance in late June.
Campaign staff in Delaware had concluded a call with state aides just minutes before Mr Biden published a letter when he announced the end of his re-election bid.
“I don’t think a soul in Delaware knew,” an official said.
Cedric Richmond, a co-chair of the Biden campaign, insisted on Sunday morning that the US President was determined to fight on and beat Donald Trump in November’s election.
“I want to be crystal clear. He’s made a decision and that decision is to accept the nomination and run for reelection, win reelection,” he told CBS News.