Two-dimensional boron (borophene) is a promising, newly synthesized monolayer metal with promising electronic and optical properties. Borophene has only been recently synthesized on silver substrates, and displays a variety of crystal structures and substrate-induced strains depending on the growth conditions and surface orientation. Here, we present an extensive first-principles study of the structural and optoelectronic properties of the two proposed structures of borophene, β12 and δ6, under strain. With a density functional theory analysis, we determine that the optical absorbance and electronic band structure are continuously tunable upon application of few percent of strain. Although both structures remain metallic with moderate strains of up to 6% applied, key features of the band structure, as well as the inplane anisotropy of the complex dielectric function and optical absorption, can be significantly modified.