Barium (Ba) stars are chemically peculiar stars that show enhanced surface abundances of heavy elements produced by the slow-neutron-capture process, the so-called s-process. These stars are not sufficiently evolved to undergo the s-process in their interiors, so they are considered products of binary interactions. Ba stars form when a former Asymptotic Giant Branch (AGB) companion, which is now a white dwarf, pollutes them with s-process-rich material through mass transfer. This paper presents a detailed chemical characterization of two newly discovered Ba giants. Our main goal is to confirm their status as extrinsic s-process stars and explore potential binarity and white dwarf companions. We obtained high-resolution spectra with UVES on the Very Large Telescope to determine the chemical properties of the targets. We perform line-by-line analyses and measure 22 elements with an internal precision up to 0.04 dex. The binary nature of the targets is investigated through radial velocity variability and spectral energy distribution fitting. We found that both targets are enhanced in all the measured s-process elements, classifying our targets as Ba giants. This is the first time they are classified as such in the literature. Additionally, both stars present a mild enhancement in Eu, but less than in pure s-process elements, suggesting that the sources that polluted them were pure s-process sources. Finally, we confirmed that the two targets are RV variable and likely binary systems. The abundances in these two newly discovered polluted binaries align with classical Ba giants, providing observational constraints to better understand the s-process in AGB stars.