For Ms. Rice, the appointment amounts to redemption after she withdrew from consideration as secretary of state because Republicans threatened to block her nomination over Benghazi.
Mr. Obama steadfastly defended Ms. Rice, and after he nominated John Kerry instead of her, White House officials said she became the front-runner to succeed Mr. Donilon, who has been in the job since October 2010 and had been the principal deputy before that.
A Rhodes Scholar who holds a doctorate in international affairs from Oxford University, Ms. Rice began her government career on the National Security Council during the Clinton administration, later serving as senior director for African affairs from 1995 to 1997.
A foreign policy adviser to then-Senator Obama during his 2008 campaign, Ms. Rice was viewed as a potential national security adviser in his first term. Mr. Obama instead sent her to the United Nations and chose Gen. James L. Jones, a former Marine Corps commandant.
At the United Nations, Ms. Rice earned good reviews for lining up balky members behind sanctions on North Korea and Iran. After Mr. Obama’s re-election, she was seen as a prime candidate to replace Mrs. Clinton. But that was before she appeared on television to discuss the attack in Benghazi, which killed four Americans, including Ambassador J. Christopher Stevens.
Ms. Rice, using talking points drafted by the C.I.A., said the assault appeared to be a protest gone awry rather than a premeditated terrorist attack. That proved incorrect, and though Ms. Rice cautioned that the account could change with further intelligence, Republicans accused her of sanitizing the truth for political reasons.
After withdrawing her name as secretary of state, Ms. Rice returned to the United Nations, where she kept a low profile, immersing herself in issues involving countries like Syria and North Korea. But she has retained the confidence of the White House, playing an influential role in internal debates over questions like whether to arm the rebels in Syria.
“When she speaks,” Mr. Biden said last month, “no one wonders whether or not she is speaking for the president.”