Gestational Diabetes Act of 2019 or the GEDI Act This bill amends the Public Health Service Act to direct the Centers for Disease Control and Prevention (CDC) to develop a multisite gestational diabetes (i.e., diabetes occuring during pregnancy) research project to expand and enhance surveillance data and public health research about gestational diabetes. The CDC must: (1) award grants for demonstration projects to reduce the incidence of gestational diabetes, the recurrence of such disease in subsequent pregnancies, and the development of type 2 diabetes in women with a history of gestational diabetes; and (2) work with state and tribal diabetes prevention and control programs assisted by the CDC to encourage postpartum follow-up after gestational diabetes to reduce the incidence of gestational diabetes and its recurrence, the development of type 2 diabetes in at-risk women, and related complications.