Although glass-forming melts exhibit a drastic change in their dynamic and thermodynamic properties at the glass-transition temperature (Tg), structural signatures of the liquid-to-glass transition remain 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 in-situ neutron scattering, we demonstrate that both short- and medium-range order structural parameters show a pronounced change of slope at Tg 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 Tg. Based on these results, we find that the slope change of the area of the first sharp diffraction peak at Tg is correlated to the extent of the CTE jump at Tg, which offers for the first time a structural origin for the discontinuity in the CTE of glasses at Tg. This study can shine light on solving critical industrial problems, such as glass relaxation.