The Gulf Stream plays an important role in North Atlantic climate variability on a range of timescales. The North Atlantic is notable for large decadal variability in sea surface temperatures (SST). Whether this variability is driven by atmospheric or oceanic influences is a disputed point. Long time series of atmospheric and ocean variables, in particular long time series of Gulf Stream position, reveal differing sources of SST variability on quasi‐decadal and multidecadal timescales. On quasi‐decadal timescales, an oscillatory signal identified in the North Atlantic Oscillation (NAO) controls SST evolution directly via air‐sea heat fluxes. However, on multidecadal timescales, this relationship between the NAO and SST changes, while the relationship between the NAO and Gulf Stream position remains consistent in phase and resonant in amplitude. Recent changes in the Gulf Stream Extension show a weakening and broadening of the current, consistent with increased instability. We consider these changes in the context of a weakening Atlantic overturning circulation. Plain Language Summary The North Atlantic Ocean is a region of remarkable variability in surface temperatures on timescales of decades and longer. Much debate surrounds whether this variability is driven by the atmosphere or by ocean currents, such as the Gulf Stream, moving heat around. In this study, we show that on timescales around 10 years, the atmosphere is the likely cause of Atlantic temperature variability but that this changes when multidecadal variability is considered. Changes ongoing in the Gulf Stream coincide with changes in the broader Atlantic—changes that imply a relatively cooler Atlantic in the coming decades. Key Points On quasi‐decadal timescales, NAO varies in phase with GSNW and in antiphase with Atlantic SSTs On multidecadal timescales, NAO continues to vary in phase with GSNW, but the relationship to Atlantic SSTs has changed The weakening and broadening of the Gulf Stream is consistent with increased instability since 2005 and not with a northward shift