Smart biomaterials that are self-assembled from peptide amphiphiles (PA) are known to undergo morphological transitions in response to specific physiological stimuli. The design of such customizable hydrogels is of significant interest due to their potential applications in tissue engineering, biomedical imaging, and drug delivery. Using a novel coarse-grained peptide/polymer model, which has been validated by comparison of equilibrium conformations from atomistic simulations, large-scale molecular dynamics simulations are performed to examine the spontaneous self-assembly process. Starting from initial random configurations, these simulations result in the formation of nanostructures of various sizes and shapes as a function of the electrostatics and temperature. At optimal conditions, the self-assembly mechanism for the formation of cylindrical nanofibers is deciphered involving a series of steps: (1) PA molecules quickly undergo micellization whose driving force is the hydrophobic interactions between alkyl tails; (2) neighboring peptide residues within a micelle engage in a slow ordering process that leads to the formation of β-sheets exposing the hydrophobic core; (3) spherical micelles merge together through an end-to-end mechanism to form cylindrical nanofibers that exhibit high structural fidelity to the proposed structure based on experimental data. As the temperature and electrostatics vary, PA molecules undergo alternative kinetic mechanisms, resulting in the formation of a wide spectrum of nanostructures. A phase diagram in the electrostatics-temperature plane is constructed delineating regions of morphological transitions in response to external stimuli.