Abstract: Recently, interlayer and intralayer excitons in transition metal dichalcogenide heterobilayers have been studied both experimentally and theoretically. In spite of a growing interest, these layer-resolved excitons in the presence of external stimuli, such as strain, remain not fully understood. Here, using density-functional theory calculations with many-body effects, we explore the excitonic properties of vertically stacked MoSe2/WSe2 heterobilayer in the presence of in-plane biaxial strain of up to 5%. We calculate the strain dependence of exciton absorption spectrum, oscillator strength, wave function, and binding energy by solving the Bethe-Salpeter equation on top of the standard GW approach. We identify the interlayer and intralayer excitons by analyzing their electron-hole weights and spatial wave functions. We show that with the increase in strain magnitude, the absorption spectrum of the interlayer and intralayer excitons is red-shifted and re-ordered, and the binding energies of these layer-resolved excitons decrease monotonically and almost linearly. We derive the sensitivity of exciton binding energy to the applied strain and find that the intralayer excitons are more sensitive to strain than the interlayer excitons. For instance, a sensitivity of -7.9 meV/% is derived for the intra-MoSe2-layer excitons, which is followed by -7.4 meV/% for the intra-WSe2-layer excitons, and by -4.2 meV/% for the interlayer excitons. Our results indicate that interlayer and intralayer excitons in vertically stacked MoSe2/WSe2 heterobilayer are efficiently tunable by in-plane biaxial strain.