Iranian Proxies Terrorist Sanctions Act of 2019 This bill directs the President to impose sanctions on As-Saib Ahl al-Haq and Harakat Hizballah al-Nujaba, two Iraqi paramilitary groups affiliated with Iran. The sanctions relate to blocking property and transactions and also apply to foreign individuals serving as the groups' officials, agents, and affiliates. The President shall submit detailed explanations as to whether sanctions should be imposed on various individuals identified in the bill. The Department of State shall annually publish a list of groups that receive logistical, military, or financial support from Iran's Islamic Revolutionary Guard Corps (IRGC) or under the IRGC's influence.