Ocean memory, the persistence of ocean conditions, is a major source of predictability in the climate system beyond weather time scales. We show that ocean memory, as measured by the year-to-year persistence of sea surface temperature anomalies, is projected to steadily decline in the coming decades over much of the globe. This global decline in ocean memory is predominantly driven by shoaling of the upper-ocean mixed layer depth in response to global surface warming, while thermodynamic and dynamic feedbacks can contribute substantially regionally. As the mixed layer depth shoals, stochastic forcing becomes more effective in driving sea surface temperature anomalies, increasing high-frequency noise at the expense of persistent signals. Reduced ocean memory results in shorter lead times of skillful persistence-based predictions of sea surface thermal conditions, which may present previously unknown challenges for predicting climate extremes and managing marine biological resources under climate change.