The solubility of H2O- and CO2-bearing fluids in tholeiitic basalts has been investigated experimentally at temperature of 1250 °C and pressures of 50, 100, 200, 300, 400 and 500 MPa. The concentrations of dissolved H2O and CO2 have been determined using FTIR spectroscopy with an accurate calibration of the absorption coefficients for hydrogen- and carbon-bearing species using synthesized standards of the same tholeiitic composition. The absorption coefficients are 0.65 ± 0.08 and 0.69 ± 0.08 L/(mol cm) for molecular H2O and OH groups by Near-Infrared (NIR), respectively, and 68 ± 10 L/(mol cm) for bulk H2O by Mid-Infrared (MIR). The carbonate groups determined by MIR have an absorption coefficient of 317 ± 23 L/(mol cm) for the band at 1430 cm−1.The solubility of H2O in the melt in equilibrium with pure H2O fluid increases from about 2.3 ± 0.12 wt.% at 50 MPa to about 8.8 ± 0.16 wt.% at 500 MPa, whereas the concentration of CO2 increases from about 175 ± 15 to 3318 ± 276 ppm in the melts which were equilibrated with the most CO2-rich fluids (with mole fraction of CO2 in the fluid, XflCO2, from 0.70 to 0.95). In melts coexisting with H2O- and CO2-bearing fluids, the concentrations of dissolved H2O and CO2 in basaltic melt show a non-linear dependence on both total pressure and mole fraction of volatiles in the equilibrium fluid, which is in agreement with previous studies. A comparison of new experimental data with existing numerical solubility models for mixed H2O–CO2 fluids shows that the models do not adequately predict the solubility of volatiles in basaltic liquids at pressures above 200 MPa, in particular for CO2, implying that the models need to be recalibrated. The experimental dataset presented in this study enables a quantitative interpretation of volatile concentrations in glass inclusions to evaluate the magma storage conditions and degassing paths of natural island arc basaltic systems. The experimental database covers the entire range of volatile compositions reported in the literature for natural melt inclusions in olivine from low- to mid-K basalts indicating that most melt inclusions were trapped or equilibrated at intermediate to shallow levels in magmatic systems (< 12–15 km).