The selection of the pair raises the question of whether Obama's foreign policy might place more emphasis on human rights issues during his second term.
Rice's appointment could anger Republicans who have sharply criticized her role in the handling of last September's attack on a U.S. diplomatic compound in Benghazi, Libya that killed four Americans, including U.S. Ambassador Christopher Stevens.
Obama had been expected to pick Rice, 48, as national security adviser since she withdrew last December from consideration to replace Hillary Clinton as secretary of state under intense criticism from Republicans about Benghazi. She had been Obama's first choice to replace Clinton, but the job instead went to John Kerry.
Rice will take over from Donilon in July as the official who coordinates U.S. foreign policy from the White House. Obama will avoid a congressional fight, though, because the post does not require Senate confirmation.
"She is at once passionate and pragmatic," Obama said, flanked by Donilon, Rice and Power in the White House Rose Garden. "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."
In her remarks, Rice did not mention the Benghazi attack or the Republican criticism. She said she looked forward to working with "our country's most experienced leaders from both parties."
Republicans have accused Rice of playing down the Benghazi incident for political purposes by initially describing it on Sunday TV news shows as the result of a spontaneous protest, rather than a terrorist attack.
Republican Senator John McCain, a leading opponent of the way Obama has handled the Benghazi controversy, tweeted that he disagreed with Rice's selection but said, "I'll make every effort" to work with her.