Strain presents a straightforward tool to tune electronic properties of atomically thin nanomaterials that are highly sensitive to lattice deformations. While the influence of strain on the electronic band structure has been intensively studied, there are only a few works on its impact on optical properties of monolayer transition-metal dichalcogenides (TMDs). Combining microscopic theory based on Wannier and Bloch equations with nearest-neighbor tight-binding approximation, we present an analytical view on how uni-and biaxial strain influences the optical fingerprint of TMDs, including their excitonic binding energy, oscillator strength, optical selection rules, and the radiative broadening of excitonic resonances. We show that the impact of strain can be reduced to changes in the lattice structure (geometric effect) and in the orbital functions (overlap effect). In particular, we demonstrate that the valley-selective optical selection rule is softened in the case of uniaxial strain due to the introduced asymmetry in the lattice structure. Furthermore, we reveal a considerable increase of the radiative dephasing due to strain-induced changes in the optical matrix element and the excitonic wave functions.