One of water's unsolved puzzles is the question of what determines the lowest temperature to which it can be cooled before freezing to ice. The supercooled liquid has been probed experimentally to near the homogeneous nucleation temperature, TH~232K, yet the mechanism of ice crystallization--including the size and structure of critical nuclei--has not yet been resolved. The heat capacity and compressibility of liquid water anomalously increase on moving into the supercooled region, according to power laws that would diverge (that is, approach infinity) at ~225K (refs 1, 2), so there may be a link between water's thermodynamic anomalies and the crystallization rate of ice. But probing this link is challenging because fast crystallization prevents experimental studies of the liquid below TH. And although atomistic studies have captured water crystallization, high computational costs have so far prevented an assessment of the rates and mechanism involved. Here we report coarse-grained molecular simulations with the mW water model in the supercooled regime around TH which reveal that a sharp increase in the fraction of four-coordinated molecules in supercooled liquid water explains its anomalous thermodynamics and also controls the rate and mechanisms of ice formation. The results of the simulations and classical nucleation theory using experimental data suggest that the crystallization rate of water reaches a maximum around 225K, below which ice nuclei form faster than liquid water can equilibrate. This implies a lower limit of metastability of liquid water just below TH and well above its glass transition temperature, 136K. By establishing a relationship between the structural transformation in liquid water and its anomalous thermodynamics and crystallization rate, our findings also provide mechanistic insight into the observed dependence of homogeneous ice nucleation rates on the thermodynamics of water.