Observations have shown that the star-formation activity and the morphology of galaxies are closely related, but the underlying physical connection is not well understood. Using the TNG50 simulation, we explore the quenching and the morphological evolution of the 102 massive quiescent galaxies in the mass range of 10.5 < log (Mstellar/M⊙) < 11.5 selected at z = 0. We show that galaxies tend to be quenched more rapidly if they: (i) are satellites in massive haloes, (ii) have lower star-forming gas fractions, or (iii) inject a larger amount of black hole kinetic feedback energy. Following global evolutionary pathways, we conclude that quiescent discs are mainly disc galaxies that are recently and slowly quenched. Approximately half of the quiescent ellipticals at z = 0 are rapidly quenched at higher redshifts while still disc-like. While quiescent, these gradually become more elliptical mostly by disc heating, yet these ellipticals still retain some degree of rotation. The other half of quiescent ellipticals with the most random motion-dominated kinematics build up large spheroidal components before quenching primarily by mergers, or in some cases, misaligned gas accretion. However, the mergers that contribute to morphological transformation do not immediately quench galaxies in many cases. In summary, we find that quenching and morphological transformation are largely decoupled. We conclude that the TNG black hole feedback – in combination with the stochastic merger history of galaxies – leads to a large diversity of quenching timescales and a rich morphological landscape.