Advancing Competency-Based Education Act of 2019 This bill requires the Department of Education to select institutions of higher education (IHE) to voluntarily carry out competency-based education demonstration projects. A competency-based education program is an alternative postsecondary program that measures academic progress and credential attainment by the assessment of student learning and the mastery of competencies instead of, or in addition to, credit hours. A participating IHE must take certain transparency and accountability measures including (1) providing information comparing the success of students in competency-based education programs to similar students in traditional programs; (2) submitting to an annual evaluation of each competency-based education program to determine quality, progress of students toward earning a degree, and students' ability to pay off loans and find employment upon graduation; and (3) aligning their courses with career pathways and the needs of local employers in order to prepare students for the workforce. The bill also establishes the Competency-Based Education Council to study the ongoing innovation and development of competency-based education programs and to develop recommendations for the authorization of such programs.