Powerful flares from blazars with short (∼min) variability time-scales are challenging for current models of blazar emission. Here, we present a physically motivated ab initio model for blazar flares based on the results of recent particle-in-cell (PIC) simulations of relativistic magnetic reconnection. PIC simulations demonstrate that quasi-spherical plasmoids filled with high-energy particles and magnetic fields are a self-consistent by-product of the reconnection process. By coupling our PIC-based results (I.e. plasmoid growth, acceleration profile, particle and magnetic content) with a kinetic equation for the evolution of the electron distribution function we demonstrate that relativistic reconnection in blazar jets can produce powerful flares whose temporal and spectral properties are consistent with the observations. In particular, our model predicts correlated synchrotron and synchrotron self-Compton flares of duration of several hours-days powered by the largest and slowest moving plasmoids that form in the reconnection layer. Smaller and faster plasmoids produce flares of sub-hour duration with higher peak luminosities than those powered by the largest plasmoids. Yet, the observed fluence in both types of flares is similar. Multiple flares with a range of flux-doubling time-scales (minutes to several hours) observed over a longer period of flaring activity (days or longer) may be used as a probe of the reconnection layer's orientation and the jet's magnetization. Our model shows that blazar flares are naturally expected as a result of magnetic reconnection in a magnetically dominated jet.