Secure and Trusted Communications Networks Act of 2019 This bill establishes (1) a mechanism to prevent communications equipment or services that pose a national security risk from entering U.S. networks, and (2) a program to remove any such equipment or services currently used in U.S. networks. Specifically, the bill prohibits the use of certain federal funds to obtain communications equipment or services from a company that poses a national security risk to U.S. communications networks. The Federal Communications Commission (FCC) must publish and maintain a list of such equipment or services. Each communications provider must submit an annual report to the FCC regarding whether it has purchased, rented, leased, or otherwise obtained any prohibited equipment and, if so, provide a detailed justification for such action. The bill also establishes the Secure and Trusted Communications Networks Reimbursement Program to supply small communications providers (i.e., providers with 2 million or fewer customers) with funds to offset the cost of removing prohibited equipment or services from their networks and replacing it with more secure communications equipment or services. In addition, the National Telecommunications and Information Administration must establish a program to share information regarding supply chain security risks with trusted communications providers and suppliers.