We present measurements and theoretical modeling demonstrating the capability of Doppler Broadened annihilation gamma Spectroscopy (DBS) to provide element-specific information from the topmost atomic layer of surfaces that are either clean or covered with adsorbates or thin films. Our measurements show that the energy spectra of Doppler-shifted annihilation gamma photons emitted following the annihilation of positrons from the topmost atomic layers of clean gold (Au) and copper (Cu) differ significantly. With the aid of the positron annihilation-induced Auger electron spectroscopy (PAES) performed simultaneously with DBS, we show that measurable differences between the Doppler broadened gamma spectra from Au and Cu surfaces in the high energy region of the gamma spectra can be used for the quantification of surface chemical composition. Modeling the measured Doppler spectra from clean Au and Cu surfaces using gamma spectra obtained from ab initio calculations after considering the detector energy resolution and surface positronium formation pointed to an increase in the relative contribution of gamma from positron annihilation with valence shell electrons. The fit result also suggests that the surface-trapped positrons predominantly annihilated with the delocalized valence shell (s and p) electrons that extended into the vacuum as compared to the highly localized d electrons. Simultaneous DBS and PAES measurements from adsorbate (sulfur, oxygen, carbon) or thin film (selenium (Se), graphene) covered Cu surface showed that it is possible to distinguish and quantify the surface adsorbate and thin-film composition just based on DBS. DBS of elemental surfaces presents a promising avenue for developing a characterization tool that can be used to probe external and internal surfaces that are inaccessible by conventional surface science techniques.