Rift Valley fever (RVF) is an emerging, zoonotic, arboviral hemorrhagic fever threatening livestock and humans mainly in Africa. RVF is of global concern, having expanded its geographical range over the last decades. The impact of control measures on epidemic dynamics using empirical data has not been assessed. Here, we fitted a mathematical model to seroprevalence livestock and human RVF case data from the 2018-2019 epidemic in Mayotte to estimate viral transmission among livestock, and spillover from livestock to humans through both direct contact and vector-mediated routes. Model simulations were used to assess the impact of vaccination on reducing the epidemic size. The rate of spillover by direct contact was about twice as high as vector transmission. Assuming 30% of the population were farmers, each transmission route contributed to 45% and 55% of the number of human infections, respectively. Reactive vaccination immunizing 20% of the livestock population reduced the number of human cases by 30%. Vaccinating 1 mo later required using 50% more vaccine doses for a similar reduction. Vaccinating only farmers required 10 times as more vaccine doses for a similar reduction in human cases. Finally, with 52.0% (95% credible interval [CrI] [42.9-59.4]) of livestock immune at the end of the epidemic wave, viral reemergence in the next rainy season (2019-2020) is unlikely. Coordinated human and animal health surveillance, and timely livestock vaccination appear to be key to controlling RVF in this setting. We furthermore demonstrate the value of a One Health quantitative approach to surveillance and control of zoonotic infectious diseases.