We investigate the origin of the Hubble sequence by analysing the evolution of the kinematic morphologies of central galaxies in the EAGLE cosmological simulation. By separating each galaxy into disk and spheroidal stellar components and tracing their evolution along the merger tree, we find that the morphology of galaxies follows a common evolutionary trend. We distinguish three phases of galaxy formation. These phases are determined primarily by mass, rather than redshift. For M_star < 10^{9.5} M_sun galaxies grow in a disorganised way, resulting in a morphology that is dominated by random stellar motions. This phase is dominated by in-situ star formation, partly triggered by mergers. In the mass range 10^{9.5} M_sun < M_star < 10^{10.5} M_sun galaxies evolve towards a disk-dominated morphology, driven by in-situ star formation. The central spheroid (i.e. the bulge) at z = 0 consists mostly of stars that formed in-situ, yet the formation of the bulge is to a large degree associated with mergers. Finally, at M_star > 10^{10.5} M_sun growth through in-situ star formation slows down considerably and galaxies transform towards a more spheroidal morphology. This transformation is driven more by the buildup of spheroids than by the destruction of disks. Spheroid formation in these galaxies happens mostly by accretion at large radii of stars formed ex-situ (i.e. the halo rather than the bulge).

18 pages (including appendices), 11 figures, 2 tables, accepted for publication in MNRAS