The confined variational method is applied to investigate the low-energy elastic scattering of orthopositronium from H2 by first-principles quantum mechanics. Describing the correlations with explicitly correlated Gaussians, we obtain accurate s-wave phase shifts and pickoff annihilation parameters for different incident momenta. By a least-squares fit of the data to the effective-range theory, we determine the s-wave scattering length AS=2.02a0 and the zero-energy value of the pickoff annihilation parameter, 1Zeff=0.1839. The obtained 1Zeff agrees well with the precise experimental value of 0.186(1) [G. L. Wright, J. Phys. B 16, 4065 (1983)10.1088/0022-3700/16/21/027] and the obtained AS agrees well with the value of 2.1(2)a0 estimated from the average experimental momentum-transfer cross section for positronium energy below 0.3 eV [F. Saito, J. Phys. B 36, 4191 (2003)10.1088/0953-4075/36/20/011].