Supercooled silicate liquids exhibit several orders of magnitude increase in viscosity at the glass-transition temperature (${T}_{\mathrm{g}}$) towards the glassy state. Such a drastic dynamical slowdown leads to an abrupt change in the slope of temperature-dependent thermodynamic properties because the measurements reflect the equilibrium-to-nonequilibrium change from liquid to glass. However, an underlying structural change associated with such a transition remains elusive. For instance, understanding the structural origin of the variation in the coefficient of thermal expansion (CTE) of silicate glasses upon vitrification is critical for glass-manufacturing processes and applications. Here, based on temperature-dependent neutron diffraction, we demonstrate that the temperature dependences of both short- and medium-range order structural parameters show a pronounced change of slope at ${T}_{\mathrm{g}}$ for a range of silicate glasses of industrial importance. Interestingly, the short- and medium-range order structural parameters are found to be mutually correlated, both below and above ${T}_{\mathrm{g}}$. Based on these results, we find that the slope change of the area of the first sharp diffraction peak at ${T}_{\mathrm{g}}$ is correlated with the extent of the CTE jump at ${T}_{\mathrm{g}}$, which offers a structural origin for the discontinuity in the CTE of glasses at ${T}_{\mathrm{g}}$. This study can therefore shine light on solving critical industrial problems, such as glass relaxation.