Veterans to Paramedics Transition Act - Amends the Public Health Service Act to: (1) include among entities eligible for rural emergency medical service training and equipment grants entities that provide training for emergency medical services personnel, including institutions of higher education, technical colleges, community colleges, and other state-certified training entities; and (2) include among grant uses the provision of required coursework and training to enable military veterans to satisfy emergency medical services personnel certification requirements, as determined by the appropriate state regulatory entity.