We report the structural, magnetic, specific heat, and electronic structure studies of the material ${\mathrm{K}}_{3}\mathrm{Yb}{({\mathrm{VO}}_{4})}_{2}$, which has two-dimensional triangular layers constituted by rare-earth magnetic ${\mathrm{Yb}}^{3+}$ ions. Magnetic susceptibility data show the absence of magnetic long-range order down to $0.5\phantom{\rule{0.16em}{0ex}}\mathrm{K}$. No bifurcation is observed between zero-field-cooled and field-cooled magnetic susceptibility data, ruling out the possibility of spin-glassiness down to $0.5\phantom{\rule{0.16em}{0ex}}\mathrm{K}$. From the fit to magnetic susceptibility data with Curie-Weiss law in the low-temperature region, the observed Curie-Weiss temperature $(\ensuremath{\theta}{}_{\mathrm{CW}})$ is about $\ensuremath{-}1\phantom{\rule{0.16em}{0ex}}\mathrm{K}$, implying an antiferromagnetic coupling between the ${\mathrm{Yb}}^{3+}$ ions. Magnetic field-dependent specific heat fits well with two-level Schottky behavior. The analysis of magnetization and specific heat data confirms that the ${\mathrm{Yb}}^{3+}$ ion hosts the effective spin ${J}_{\mathrm{eff}}=1/2$ state. To provide a microscopic understanding of the ground state nature of the titled material, we carried out state-of-the-art first-principles calculations based on density functional theory $+$ Hubbard U and density functional theory $+$ dynamical mean-field theory approaches. Our calculations reveal that the system belongs to the novel class of spin-orbit driven Mott Hubbard insulators and possesses large in-plane magnetocrystalline anisotropy.