A comprehensive analysis of subionospheric Very Low Frequency (VLF) signals from transmitters with call‐signs NWC, NPM, and NLK monitored at a low‐latitude station, Suva, Fiji, has been carried out to determine the D‐region effects of the intense geomagnetic storms for a period of 7 years (2011–2016 and 2018). The periods of 2011–2016 and 2018 fall under the 24th solar cycle with yearly mean sunspot numbers 80.8–39.8 and 7.0, respectively. Seven out of 12 geomagnetic storms revealed VLF anomalies during the storm main phase day and storm recovery phase days. A pronounced decrease in the VLF amplitude and phase for the storms having main phase onset in the nighttime was found. Out of seven geomagnetic storms, a storm of St Patrick's Day of 17–18 March 2013 is presented as a case study and the same analysis was done for all the storms. The anomalies in the VLF amplitude and phase have been modeled using Long‐Wave Propagation Capability code V2.1 to obtain the changes in Wait parameters (reference height, H′ and sharpness factor, ꞵ) and changes in the D‐region electron density. In most cases of storms, an increase in the H′ and a decrease in the ꞵ during the storm main and recovery phases were obtained which for the 17–18 March 2013 storm increased by 7.4–7.6 km and decreased from 0.03 to 0.07 km−1, respectively. Wavelet analysis of signal anomalies showed clear wave‐like spectra (0.05–0.18 mHz) of atmospheric gravity waves indicating traveling ionospheric disturbances propagating toward low latitudes due to storm‐associated Joule heating at high latitudes.