Between January 2013 and December 2014, water levels on Lake Superior and Lake Michigan-Huron, the two largest lakes on Earth by surface area, rose at the highest rate ever recorded for a 2 year period beginning in January and ending in December of the following year. This historic event coincided with below-average air temperatures and extensive winter ice cover across the Great Lakes. It also brought an end to a 15 year period of persistently below-average water levels on Lakes Superior and Michigan-Huron that included several months of record-low water levels. To differentiate hydrological drivers behind the recent water level rise, we developed a Bayesian Markov chain Monte Carlo (MCMC) routine for inferring historical estimates of the major components of each lake's water budget. Our results indicate that, in 2013, the water level rise on Lake Superior was driven by increased spring runoff and over-lake precipitation. In 2014, reduced over-lake evaporation played a more significant role in Lake Superior's water level rise. The water level rise on Lake Michigan-Huron in 2013 was also due to above-average spring runoff and persistent over-lake precipitation, while in 2014, it was due to a rare combination of below-average evaporation, above-average runoff and precipitation, and very high inflow rates from Lake Superior through the St. Marys River. We expect, in future research, to apply our new framework across the other Laurentian Great Lakes, and to Earth's other large freshwater basins as well.