Rice will step into the security adviser's role when Donilon leaves in July, Obama said.
Rice will be replaced by Samantha Power, who served on Obama's security team during his first term, the president said.
Obama said he has leaned heavily on Donilon's counsel the past several years.
"He's definitely advanced our strategic foreign policy initiatives, while at the same time having to respond to unexpected crises, and that happens just about every day," Obama said.
"He's overseen and coordinated our entire national security team across the government, a Herculean task -- and it's non-stop, 24/7, 365 days a year.
"He shared my view that in order to renew American leadership for the 21st century, we had to fundamentally rebalance our foreign policy. And more than that, he knew how we could do it."
Obama said he is "absolutely thrilled" to have Rice on his White House team.
"She is at once passionate and pragmatic," he said. "I think everybody understands Susan is a fierce champion for justice and human dignity. But she's also mindful that we have to exercise our power wisely and deliberately."
"Having served on the National Security Council staff herself, she knows how to bring people together around a common policy and then push it through to completion, so that we're making a difference where it matters most here in the country that we pledged to defend and in the daily lives of people we're trying to help around the world.
"Having served as an assistant secretary of state, she knows our policies are stronger when we harness the views and talents of people across government.
"So Susan's the consummate public servant."
Obama called Power "one of our foremost thinkers on foreign policy."
"As a senior member of my national security team, she's been a relentless advocate for American interests and values, building partnerships on behalf of democracy and human rights, fighting the scourge of anti-Semitism and combating human trafficking," he said.
White House press secretary Jay Carney told reporters at Wednesday's daily briefing Rice's appointment has drawn "an enormous amount of positive reaction." He cited statements by Republican U.S. Sens. John McCain of Arizona, Lindsey Graham of South Carolina and Kelly Ayotte of New Hampshire -- "who obviously have played a role in the discussions about the Benghazi talking points, saying that they will be working with her as national security adviser."
Carney said the appointments do not signal a change in administration policy on the civil war in Syria.
Rice, whose possible appointment as secretary of state after Hillary Clinton resigned was torpedoed by heavy Republican congressional opposition, will not need Senate confirmation for the security adviser's post.
Rice, 48, has been a magnet for Republican criticism for presenting an erroneous account -- during Sunday talk show appearances -- of the Sept. 11, 2012, attack on the U.S. Consulate in Benghazi, Libya, in which Ambassador Christopher Stevens and three other diplomatic staffers were killed.
Donilon, 58, exerted influence on issues such as counter-terrorism, the refocus of America to Asia and the wars in Afghanistan and Iraq.
An uncomplimentary profile published recently in Foreign Policy magazine portrayed him as an infighter and a domineering boss with strained relationships with colleagues, including former NSA deputy Denis R. McDonough, now the White House chief of staff. Donilon and McDonough have denied the reports.
The New York Times reported Donilon said he had planned to leave after Obama's first term but remained at the president's request to assist with the new team led by Secretary of State John Kerry, Defense Secretary Chuck Hagel and CIA chief John Brennan.
Reaction to Rice's appointment was shaded along party lines.
"She's going to have her plate full if she's chosen," The Washington Post quoted Graham as saying ahead of the announcement. "I will not be petty. I will put my differences on Benghazi aside and work with her."
Sen. Bob Casey, D-Pa., said in a statement he strongly supports Rice's selection.
"Susan has been a tough diplomat and an effective representative of the United States at the U.N. and throughout her distinguished career," Casey said. "I am proud to call Susan a friend and look forward to working with her in this new role.
"The president and the country will be well-served with her counsel and leadership as we face a host of growing security challenges around the world."