Climate conditions play a key role in determining the occurrence and severity of wildfires. Despite the impacts of wildfires on ecosystems, human livelihoods, and air quality, little is known conceptually about how natural or anthropogenic shifts in climate may influence the fire activity on a regional or global scale. Here, we introduce a new low order dynamical model that describes the nonlinear interactions between climate, vegetation (fire fuel) and fire probabilities. This 1-dimensional model describes the influence of precipitation and temperature on burned area and fuel availability. Estimating key parameters from observations, the model successfully reproduces the spatio-temporal variability of wildfire occurrences, particularly, in semi-arid regions in Africa, South America, and northern Australia. The fidelity of the model translates into a high degree of longer-term predictability of fire conditions in these vulnerable regions. Our new low-order modeling framework may provide guidance to forestry managers to assess fire risks under present and future climate conditions.