Rift Valley fever (RVF) is a major zoonotic and arboviral hemorrhagic fever. The conditions leading to RVF epidemics are still unclear, and the relative role of climatic and anthropogenic factors may vary between ecosystems. Here, we estimate the most likely scenario that led to RVF emergence on the island of Mayotte, following the 2006-2007 African epidemic. We developed the first mathematical model for RVF that accounts for climate, animal imports and livestock susceptibility, which is fitted to a 12-years dataset. RVF emergence was found to be triggered by the import of infectious animals, whilst transmissibility was approximated as a linear or exponential function of vegetation density. Model forecasts indicated a very low probability of virus endemicity in 2017, and therefore of re-emergence in a closed system (i.e. without import of infected animals). However, the very high proportion of naive animals reached in 2016 implies that the island remains vulnerable to the import of infectious animals. We recommend reinforcing surveillance in livestock, should RVF be reported is neighbouring territories. Our model should be tested elsewhere, with ecosystem-specific data.