Stellar population and stellar kinematic studies provide unique but complementary insights into how galaxies build-up their stellar mass and angular momentum 1-3 . A galaxy's mean stellar age reveals when stars were formed, but provides little constraint on how the galaxy's mass was assembled. Resolved stellar dynamics 4 trace the change in angular momentum due to mergers, but major mergers tend to obscure the effect of earlier interactions 5 . With the rise of large multi-object integral field spectroscopic surveys, such as SAMI 6 and MaNGA 7, and single-object integral field spectroscopic surveys (for example, ATLAS3D (ref. 8 ), CALIFA 9, MASSIVE 10 ), it is now feasible to connect a galaxy′s star formation and merger history on the same resolved physical scales, over a large range in galaxy mass, morphology and environment 4,11,12 . Using the SAMI Galaxy Survey, here we present a combined study of spatially resolved stellar kinematics and global stellar populations. We find a strong correlation of stellar population age with location in the (V/σ, ϵe) diagram that links the ratio of ordered rotation to random motions in a galaxy to its observed ellipticity. For the large majority of galaxies that are oblate rotating spheroids, we find that characteristic stellar age follows the intrinsic ellipticity of galaxies remarkably well.