Using nuclear magnetic resonance and quasi-elastic neutron scattering spectroscopic techniques, we obtain experimental evidence of a well-defined dynamic crossover temperature T-L in supercooled water. We consider three different geometrical environments: (i) water confined in a nanotube (quasi-one-dimensional water), (ii) water in the first hydration layer of the lysozyme protein (quasi-two-dimensional water), and (iii) water in a mixture with methanol at a methanol molar fraction of x = 0.22 (quasi-three-dimensional water). The temperature predicted using a power law approach to analyze the bulk water viscosity in the super-Arrhenius regime defines the fragile-to-strong transition and the Stokes-Einstein relation breakdown recently observed in confined water. Our experiments show that these observed processes are independent of the system dimension d and are instead caused by the onset of an extended hydrogen-bond network that governs the dynamical properties of water as it approaches dynamic arrest.