Structural, magnetic, and Co K-edge X-ray absorption near-edge structure (XANES) spectroscopic studies for the stoichiometric La1-xEuxCoO3 (0≦x≦1) system with trivalent Co^3+ are reported. The thermally-excited spin-state transition from low-spin (LS) to intermediate-spin (IS) state increases from T(subscript s)~105 K for LaCoO3 (x = 0) to~140 K for x = 0.25, to~200 K for x = 0.5, and extrapolates to~295 K for EuCoO3 (x = 1), where the IS state is a mixture of d^6 (t^5(subscript 2g)e^1(subscript g)) and d^7 L (t^5(subscript 2g)e^2(subscript g) with a ligand hole) with filled t(subscript 2g) majority spin states. The small pre-edge feature observed in room temperature XANES for the system in the IS state is from the 1s-3d quadrupole transition, which is weakly allowed through the hybridization of Co 4p states with 3d states of the neighboring Co atoms. For LaCoO3, the pre-edge can be fitted using three Gaussian peaks with energy separations △E(P2-P1) = 2.0 eV and △E(P3-P2) = 1.5 eV, where P1, P2, and P3 presumably correspond to the unfilled t(subscript 2g) minority, e(subscript g) majority, and e(subscript g) minority spin states, respectively.