The Apache Point Observatory Galactic Evolution Experiment (APOGEE) provides spectroscopic information of regions of the inner Milky Way, which are inaccessible to optical surveys. We present the first large study of the metallicity distribution of the innermost Galactic regions based on high-quality measurements for 7545 red giant stars within 4.5 kpc of the Galactic center, with the goal to shed light on the structure and origin of the Galactic bulge. Stellar metallicities are found, through multiple Gaussian decompositions, to be distributed in several components, which is indicative of the presence of various stellar populations such as the bar or the thin and the thick disks. Super-solar ([Fe/H] = +0.32) and solar ([Fe/H] = +0.00) metallicity components, tentatively associated with the thin disk and the Galactic bar, respectively, seem to be major contributors near the midplane. A solar-metallicity component extends outwards in the midplane but is not observed in the innermost regions. The central regions (within 3 kpc of the Galactic center) reveal, on the other hand, the presence of a significant metal-poor population ([Fe/H] = ‑0.46), tentatively associated with the thick disk, which becomes the dominant component far from the midplane (| Z| ≥slant +0.75 kpc). Varying contributions from these different components produce a transition region at +0.5 kpc ≤slant | Z| ≤slant +1.0 {kpc}, characterized by a significant vertical metallicity gradient.