It's a move aimed at repairing America's tarnished reputation. The U.S. has held over 700 "enemy combatants" – many of them without charge – in a legal black hole for seven years.
But closing the detention center will involve finding a way through a labyrinth of legal tangles – and Mr. Obama may not be able to get it accomplished in the first 100 days.
(Just hours after his inauguration, Obama ordered a 120-day halt to the ongoing terror tribunals at Guantanamo, to give his team a chance to examine the process and come up with a possible alternative.)
The Obama Administration needs time to formulate a detailed plan for closing the base and to negotiate with foreign leaders to accept detainees who cannot return to their home countries, and freezing the military tribunals gives it time to do that, while making sure no more harm is done.
To close Guantanamo and remove the remaining 250 detainees, Mr. Obama will have to address several issues: deciding what to do with 100 or so dangerous detainees; relocating the 50 detainees who have been cleared for release and finding countries to accept them where they won't be tortured or persecuted; and deciding what kind of trials to have for those who have committed crimes, some of whom have admitted involvement in the 9/11 attacks.
(Click here to read an earlier analysis of Obama's Guantanamo predicament by CBS News legal analyst Andrew Cohen.)
Several European nations have offered to admit detainees who have been cleared for release.
The Obama administration will also have to work with Congress to overturn the laws that have created the troubled military commissions and decide whether or not to pursue investigations into alleged war crimes committed by the Bush Administration.
The Obama administration is likely to work with Sen. Dianne Feinstein, the new head of the Intelligence Committee, who has a bill for closing Guantanamo which sets a one-year deadline to try or release the detainees, and which would require the C.I.A. to report all detainees to the International Red Cross.
Mr. Obama has made closing Guantanamo a priority. But it won't be easy to untangle the legal knot that the Bush administration has left him.