We have studied the temperature dependence of the crystal and magnetic structures of the Jahn-Teller distorted transition metal difluorides CrF₂ and CuF₂ by neutron powder diffraction in the temperature range 2-280 K. The lattice parameters and the unit cell volume show magnetoelastic effects below the Néel temperature. The lattice strain due to the magnetostriction effect couples with the square of the order parameter of the antiferromagnetic phase transition. We also investigated the temperature dependence of the Jahn-Teller distortion, which does not show any significant effect at the antiferromagnetic phase transition but increases linearly with increasing temperature for CrF₂, and remains almost independent of temperature in CuF₂. The magnitude of magnetovolume effect seems to increase with the low temperature saturated magnetic moment of the transition metal ions but the correlation is not at all perfect.