The Mu2e experiment at Fermilab searches for the charged-lepton flavor violating neutrino-less conversion of a negative muon into an electron in the field of a aluminum nucleus. The dynamic of such a process is well modeled by a two-body decay, resulting in a monoenergetic electron with an energy slightly below the muon rest mass (104.967 MeV). The calorimeter of this experiment plays an important role to provide excellent particle identification capabilities and an online trigger filter while aiding the track reconstruction capabilities. The baseline calorimeter configuration consists of two disks each made with about 700 undoped CsI crystals read out by two large area UV-extended Silicon Photomultipliers. These crystals match the requirements for stability of response, high resolution and radiation hardness. In this paper we present the final calorimeter design.