Using results from the Herschel Astrophysical Terrahertz Large-Area Survey (H-ATLAS) and the Galaxy and Mass Assembly (GAMA) project, we show that, for galaxy masses above ≃ 108 M⊙, 51 per cent of the stellar mass-density in the local Universe is in early-type galaxies (ETGs; Sérsic n > 2.5) while 89 per cent of the rate of production of stellar mass-density is occurring in late-type galaxies (LTGs; Sérsic n < 2.5). From this zero-redshift benchmark, we have used a calorimetric technique to quantify the importance of the morphological transformation of galaxies over the history of the Universe. The extragalactic background radiation contains all the energy generated by nuclear fusion in stars since the big bang. By resolving this background radiation into individual galaxies using the deepest far-infrared survey with the Herschel Space Observatory and a deep near-infrared/optical survey with the Hubble Space Telescope (HST), and using measurements of the Sérsic index of these galaxies derived from the HST images, we estimate that ≃83 per cent of the stellar mass-density formed over the history of the Universe occurred in LTGs. The difference between this value and the fraction of the stellar mass-density that is in LTGs today implies there must have been a major transformation of LTGs into ETGs after the formation of most of the stars.