This paper presents a physics-based analytical model for the MOS transistor operating continuously from room temperature down to liquid-helium temperature (4.2 K) from depletion to strong inversion and in the linear and saturation regimes. The model is developed relying on the 1-D Poisson equation and the drift-diffusion transport mechanism. The validity of the Maxwell-Boltzmann approximation is demonstrated in the limit to 0 K as a result of dopant freezeout in cryogenic equilibrium. Explicit MOS transistor expressions are then derived, including incomplete dopant ionization, bandgap widening, mobility reduction, and interface charge traps. The temperature dependence of the interface trapping process explains the discrepancy between the measured value of the subthreshold swing and the thermal limit at deep-cryogenic temperatures. The accuracy of the developed model is validated by experimental results on long devices of a commercial 28-nm bulk CMOS process. The proposed model provides the core expressions for the development of physically accurate compact models dedicated to low-temperature CMOS circuit simulation.