Arid and semi-arid regions are vulnerable to natural disturbances and particularly, to anthropogenic climate change. In these regions, water resources are scarce, and groundwater is commonly the main source of water for municipal supply, agricultural, and industrial purposes. Groundwater overexploitation is a common issue for these regions, where overextraction, climate variability and recharge are responsible for groundwater storage evolution. This study aims to find teleconnections through wavelet analysis between annual rates of change in storage, obtained from geostatistical groundwater modeling, and climate variability. Continuous wavelet transform, cross-wavelet analysis and wavelet coherence were used to analyze and characterize non-stationary patterns of variability of precipitation (PP), standardized precipitation index (SPI), minimum (Min_Temp) and maximum temperature (Max_Temp), Enhanced Vegetation Index (EVI), the Oceanic Niño Index (ONI), the Pacific-North American pattern (PNA), the Caribbean Index (CAR) and Groundwater Change in Storage (ΔGS) semestral time series. The results suggest significant influences of the indices on ΔGS, PP, Min_Temp and EVI. PNA manifested an important influence in short periods (2-4 years) in all aquifers, ONI showed influence mainly over long periods (8-16 years) and CAR had influence in periods of high hurricane activities. In addition, under extreme climatic conditions (El Niño or La Niña) the higher/lower water demand increase their influence on groundwater level response creating an indirect link between climate indices and ΔGS. This research can serve as a good indicator of the climate variations behavior and can provide information to understand the regional climate effects of the ENSO phenomenon in overexploited aquifers.