Using three-dimensional magnetohydrodynamic simulations, including the effects of radiative cooling/heating, chemical reactions, and thermal conduction, we investigate the formation of molecular clouds in the multi-phase interstellar medium. As suggested by recent observations, we consider the formation of molecular clouds due to accretion of H I clouds. Our simulations show that the initial H I medium is piled up behind the shock waves induced by accretion flows. Since the initial medium is highly inhomogeneous as a consequence of thermal instability, a newly formed molecular cloud becomes very turbulent owing to the development of the Richtmyer-Meshkov instability. The kinetic energy of the turbulence dominates the thermal, magnetic, and gravitational energies throughout the entire 10 Myr evolution. However, the kinetic energy measured using CO-fraction-weighted densities is comparable to the other energies, once the CO molecules are sufficiently formed as a result of UV shielding. This suggests that the true kinetic energy of turbulence in molecular clouds as a whole can be much larger than the kinetic energy of turbulence estimated using line widths of molecular emission. We find that clumps in a molecular cloud show the following statistically homogeneous evolution: the typical plasma beta of the clumps is roughly constant left angle bracketbetaright angle bracket Asymptotically = to 0.4; the size-velocity dispersion relation is Deltav Asymptotically = to 1.5 km s super(-1) (l/1 pc) super(0.5), irrespective of the density; the clumps evolve toward magnetically supercritical, gravitationally unstable cores; and the clumps seem to evolve into cores that satisfy the condition for fragmentation into binaries. These statistical properties may represent the initial conditions of star formation.