Finality of Criminal Judgments Act - Amends the Federal judicial code to condition consideration of a habeas corpus claim by a prisoner on a showing of actual prejudice resulting from the Federal right violated and that: (1) State or Federal Government action precluded assertion of that right; (2) the Federal right did not previously exist; or (3) the factual basis of the claim could not have been discovered by reasonable diligence.

Establishes a one-year statute of limitations for habeas corpus actions brought by State prisoners, and a two-year statute of limitations for similar motions made by Federal prisoners.

Vests authority to issue certificates for probable cause for appeal of habeas corpus orders exclusively in the courts of appeals.

Permits denial on the merits of habeas corpus writs notwithstanding the failure to exhaust State remedies.

Prohibits the granting of a habeas corpus writ with respect to any claim which has been fully and fairly adjudicated in State proceedings.