The WFIRST-AFTA coronagraph instrument takes advantage of AFTAs 2.4-meter aperture to provide novel exoplanet imaging science at approximately the same instrument cost as an Explorer mission. The AFTA coronagraph also matures direct imaging technologies to high TRL for an Exo-Earth Imager in the next decade. The coronagraph Design Reference Mission (DRM) optical design is based on the highly successful High Contrast Imaging Testbed (HCIT), with modifications to accommodate the AFTA telescope design, service-ability, volume constraints, and the addition of an Integral Field Spectrograph (IFS). In order to optimally satisfy the three science objectives of planet imaging, planet spectral characterization and dust debris imaging, the coronagraph is designed to operate in two different modes: Hybrid Lyot Coronagraph or Shaped Pupil Coronagraph. Active mechanisms change pupil masks, focal plane masks, Lyot masks, and bandpass filters to shift between modes. A single optical beam train can thus operate alternatively as two different coronagraph architectures. Structural Thermal Optical Performance (STOP) analysis predicts the instrument contrast with the Low Order Wave Front Control loop closed. The STOP analysis was also used to verify that the optical/structural/thermal design provides the extreme stability required for planet characterization in the presence of thermal disturbances expected in a typical observing scenario. This paper describes the instrument design and the flow down from science requirements to high level engineering requirements.