Terrorist Detention and Prosecution Act of 2010 - Replaces the term "unprivileged enemy combatant" in federal military law with the term "unlawful enemy combatant." Includes in the definition, and therefore makes subject to trial by military commissions, an individual who: (1) is closely associated with or has provided material support to al Qaeda or any other organization dedicated to committing acts of terrorism against the United States; (2) has taken up or conspired to take up arms on behalf of al Qaeda; and (3) has committed or conspired to commit acts of terrorism against the United States or American citizens or targets, regardless of the location of the individual's capture.
Allows the President to authorize the detention of any unlawful enemy combatant until determining that the individual is no longer a threat to the United States or its allies.