Geomagnetic storms have very profound effects on the Total Electron Content (TEC) of the ionosphere. In order to investigate the equatorial and low-latitude ionospheric response to the geomagnetic storms of varying intensities, a detailed study of vertical TEC (VTEC) variations resulting from Global Positioning System (GPS) data acquired at four GPS stations in Nepal along 80°–90° E longitude and 26°–30° N latitude sector has been carried out in the present work. The results were analyzed with other favorable inducing factors (solar wind parameters and geomagnetic indices) affecting TEC to constrain the causative factor. Positive phases are observed for all the storms studied. During the severe geomagnetic activity, the deviation was ~18 TECU, while it was recorded ~12 TECU and ~8 TECU during moderate and minor geomagnetic activity, respectively. The Detrended Cross-Correlation Analysis (DXA) illustrates that the value of the hourly average VTEC of the BESI station was found to have a strong positive correlation with other stations in all types of storm events, indicating a similar response of all stations towards the space weather events. In addition, the correlation of VTEC with solar wind parameters and geomagnetic indices illustrated that the VTEC shows a strong positive association with solar wind velocity (Vsw) in all three geomagnetic events. In contrast, the correlation of plasma density (Nsw), interplanetary magnetic field (IMF-Bz), the symmetric horizontal component of geomagnetic field (SYM-H), and Geomagnetic Auroral Electrojet (AE) index with VTEC vary with the intensity of the storm. Overall results of the study have revealed the characteristic features of TEC variation over Nepal regions during magnetic storms, which validates earlier research on ionospheric responses to geomagnetic storms and theoretical assumptions.