Diagnosing potential predictability of global crop yields in the near term is of utmost importance for ensuring food supply and preventing socio-economic consequences. Previous studies suggest that a substantial proportion of global wheat yield variability depends on local climate and larger-scale ocean-atmospheric patterns. The science is however at its infancy to address whether synergistic variability and volatility (major departure from the normal) of multi-national crop yields can be potentially predicted by larger-scale climate drivers. Here, using observed data on wheat yields for 85 producing countries and climate variability from 1961-2013, we diagnose that wheat yields vary synergistically across key producing nations and can also be concurrently volatile, as a function of shared larger-scale climate drivers. We use a statistical approach called robust Principal Component Analysis (rPCA), to decouple and quantify the leading modes (PC) of global wheat yield variability where the top four PCs explain nearly 33% of the total variance. Diagnostics of PC1 indicate previous year's local Air Temperature variability being the primary influence and the tropical Pacific Ocean being the most dominating larger-scale climate stimulus. Results also demonstrate that world-wide yield volatility has become more common in the current most decades, associating with warmer northern Pacific and Atlantic oceans, leading mostly to global supply shortages. As the world warms and extreme weather events become more common, this diagnostic analysis provides convincing evidence that concurrent variability and world-wide volatility of wheat yields can potentially be predicted, which has major socio-economic and commercial importance at the global scale, underscoring the urgency of common options in managing climate risk.