Multi-hazard events can be associated with larger socio-economic impacts than single-hazard events. Understanding the spatio-temporal interactions that characterize the former is therefore of relevance to disaster risk reduction measures. Here, we consider two high-impact hazards, namely wet and dry hydrological extremes, and quantify their global co-occurrence. We define these using the monthly self-calibrated Palmer Drought Severity Index based on the Penman-Monteith model (sc_PDSI_pm), covering the period 1950-2014, at 2.5 degrees horizontal resolution. We find that the land areas affected by extreme wet, dry, and wet-dry events (i.e. geographically remote yet temporally co-occurring wet or dry extremes) are all increasing with time, the trends of which in dry and wet-dry episodes are significant (p value << 0.01). The most geographically widespread wet-dry event was associated with the strong La Nina in 2010. This caused wet-dry anomalies across a land area of 21 million km(2) with documented high-impact flooding and drought episodes spanning diverse regions. To further elucidate the interplay of wet and dry extremes at a grid cell scale, we introduce two new metrics: the wet-dry (WD) ratio and the extreme transition (ET) time intervals. The WD ratio measures the relative occurrence of wet or dry extremes, whereas ET quantifies the average separation time of hydrological extremes with opposite signs. The WD ratio shows that the incidence of wet extremes dominates over dry extremes in the USA, northern and southern South America, northern Europe, north Africa, western China, and most of Australia. Conversely, dry extremes are more prominent in most of the remaining regions. The median ET for wet to dry is similar to 27 months, while the dry-to-wet median ET is 21 months. We also evaluate correlations between wet-dry hydrological extremes and leading modes of climate variability, namely the El Nina-Southern Oscillation (ENSO), Pacific Decadal Oscillation (PDO), and Atlantic Multi-decadal Oscillation (AMO). We find that ENSO and PDO have a similar influence globally, with the former significantly impacting (p value < 0.05) a larger area (18.1 % of total sc_PDSI_pm area) compared to the latter (12.0 %), whereas the AMO shows an almost inverse pattern and significantly impacts the largest area overall (18.9 %). ENSO and PDO show the most significant correlations over northern South America, the central and western USA, the Middle East, eastern Russia, and eastern Australia. On the other hand, the AMO shows significant associations over Mexico, Brazil, central Africa, the Arabian Peninsula, China, and eastern Russia. Our analysis brings new insights on hydrological multi-hazards that are of relevance to governments and organizations with globally distributed interests. Specifically, the multi-hazard maps may be used to evaluate worst-case disaster scenarios considering the potential co-occurrence of wet and dry hydrological extremes.