Swire served as a privacy official in the Clinton administration and is currently leading industry negotiations to enable Internet users to opt out of online tracking. Stone is a law professor and constitutional scholar. He clerked for liberal Supreme Court Justice William Brennan and is a member of National Advisory Council of the American Civil Liberties Union (ACLU).
ABC News reported on the group last week, but did not identify Stone as one of the members.
"These individuals bring to the task immense experience in national security, intelligence, oversight, privacy and civil liberties," Jay Carney, the White House press secretary, said in a statement.
"The Review Group will bring a range of experience and perspectives to bear to advise the President on how, in light of advancements in technology, the United States can employ its technical collection capabilities in a way that optimally protects our national security and advances our foreign policy while respecting our commitment to privacy and civil liberties, recognizing our need to maintain the public trust, and reducing the risk of unauthorized disclosure," he added.
At the meeting, Obama thanked the members of the group and told them he looks forward to hearing from them, according to Carney.
Obama announced his intent to form the review group at a press conference earlier this month. He argued that the surveillance programs are critical to national security, but he acknowledged that some changes might be necessary to restore public trust.
He said the "independent group" would be made up of a "high-level group of outside experts."
The White House said that within 60 days of beginning its work, the group will brief the president "through the Director of National Intelligence" on its preliminary findings. Privacy advocates have expressed concern about how much control Director of National Intelligence James Clapper will have over the group. But the White House has insisted that Clapper is not leading the group or directing its efforts.
The review group will provide a final report of its recommendations to the president by Dec. 15.
—Updated at 12:47 p.m.