Combating Transnational Criminal Organizations Act of 2019 or the Combating TCOs Act of 2019 This bill establishes programs designed to enhance border security and modifies the Border Enforcement Security Task Force program. The bill establishes within the Department of Homeland Security (DHS) the Integrated Border Enforcement Team (IBET) and the Border Tunnel Task Force program (BTTF). IBET shall seek to work with Canada to enhance security on the U.S.-Canada border, by (1) strengthening security between designated ports of entry; (2) detecting, preventing, and responding to border security-related violations of law; and (3) executing coordinated border security activities with Canada. BTTF shall seek to enhance efforts to identify, reduce, and remediate cross-border tunnel threats by promoting collaboration and information sharing between federal, state, local, and tribal law enforcement agencies. DHS may establish IBET and BTTF units comprised of DHS personnel, U.S. and foreign law enforcement, and other personnel as necessary to carry out each program's duties. The bill modifies the purpose of the Border Enforcement Security Task Force to include detecting, preventing, and responding to border security-related violations of law.