We combine density functional theory within the local density approximation, the quasiharmonic approximation, and vibrational density of states to calculate single crystal elastic constants, and bulk and shear moduli of diamond at simultaneous high pressures and temperatures in the ranges of 0–500 GPa and 0–4800 K. Comparison with experimental values at ambient pressure and high temperature shows an excellent agreement with our first-principles results validating our method. We show that the anisotropy factor of diamond increases to 40% at high pressures and becomes temperature independent.