Future climate predictions by global circulation models in the Coupled Model Intercomparison Project Phase 3 (CMIP3) archive indicate that the recent poleward shift of the eddy‐driven jet streams will continue throughout the 21st century. Here it is shown that differences in the projected magnitude of the trend in the Southern Hemisphere are well correlated with biases in the latitude of the jet in the simulation of 20th century climate. Furthermore, the latitude of the jet in the models’ 20th century climatology is correlated with biases in the internal variability of the jet stream, as quantified by the time scale of the annular mode. Thus an equatorward bias in the position of the jet is associated with both enhanced persistence of the annular mode, and an increased poleward shift of the jet. These relationships appear to be robust throughout the year except in the austral summer, when differences in forcing, particularly stratospheric ozone, make it impossible to compare the response of one model with another. These results suggest that the fidelity of a model’s simulation of the 20th century climate may be related to its fitness for climate prediction. The cause of this relationship is discussed, as well as the implications for climate change projections.