Although the United States has maintained complete and uninterrupted control of Guantanamo for over 100 years, the Government’s view is that the Constitution has no effect there, at least as to noncitizens, because the United States disclaimed formal sovereignty in its 1903 lease with Cuba. The Nation’s
basic charter cannot be contracted away like this. The Constitution grants Congress and the President the power to acquire, dispose of, and govern territory, not the power to decide when and where its terms apply.

The Supreme Court has ruled that Habeas applies in Gitmo... The Military Commissions Act was unconstitutional because it did not provide an adequate process for detainees. This mostly means there will be more hearings to determine what sort of legal process is required. The right is likely to likely to blow their collective top on this. Scalia starts things off in his dissent:

[This decision] will almost certainly cause more Americans to be killed... The Nation will live to regret what the Court has done today. I dissent.

In general these judges "respectfully dissent" as Roberts did...

The Volokh Conspiracy - BREAKING - Gov't Loses Boumediene 5-4: