Magnetostriction experiments have been performed at temperatures in and above the antiferromagnetic phase of ${\mathrm{EuTiO}}_{3}$. For magnetic fields below the spin-flop transition the magnetostriction is large and negative and changes to small and positive for fields exceeding this threshold. At the antiferromagnetic phase transition temperature a steep anomaly in the thermal expansion is observed in zero field which broadens and moves to lower temperature with increasing field strength. A small but well resolved anisotropy in the longitudinal and transverse field configurations of the magnetostriction is observed at low temperatures, which rapidly vanishes with increasing temperature. The crossover field where the magnetostriction changes sign coincides with the field strength where the dielectric constant adopts normal quantum paraelectric behavior and signifies strong magnetoelectric coupling to be its origin.