Sunset Act of 2019 This bill revises requirements governing congressional review of agency rules. Before implementing a new rule, agencies must (1) report to the Government Accountability Office on their rules, and (2) obtain congressional approval of the rule. The bill redefines rule to exclude (1) a rule of particular applicability (e.g., a rule that approves corporate or financial structures); (2) a rule relating to agency management or personnel; or (3) a rule of agency organization, procedure, or practice that does not substantially affect the rights or obligations of nonagency parties. This bill permits judicial review of whether an agency has completed the necessary requirements for a rule to take effect. The bill terminates an agency rule 10 years after it was approved by Congress. The President may exempt a rule from termination if such rule is (1) necessary because of an imminent threat to health or safety or other emergency, for the enforcement of criminal law, or for national security; or (2) issued to implement an international trade agreement. The bill also requires each agency, each year for 10 years, to designate for review at least 10% of all agency rules in effect on the enactment date of this bill. Further, the bill terminates any agency rule that is in effect on the enactment date of this bill but that was not extended by Congress during the 10 years subsequent to such enactment date.