Strain engineering has widely been recognized as a highly sensitive and effective way to modulate the physical properties of materials. Here, we thoroughly investigate the effects of biaxial strain-driven optoelectronic properties and thermodynamic stability of BX (XP and As) monolayers under a density functional framework. The electronic bandgap at the K-point of these materials increases with tensile (0 to +10%) strain and decreases in the presence of compressive (−10% to 0) strain. The phonon modes indicate that monolayer BP becomes thermodynamically unstable with larger than 4% compressive strain, and BAs loses stability at 4% compressive strain. However, both structures can show quite stable nature for up to + 8% tensile strain. In the presence of compressive strain, the longitudinal optical (LO) and transverse optical (TO) phonon modes become softening in nature. In contrast, it displays hardening behavior with the tensile strain in these materials. Also, superior light absorption near the infrared and visible light spectrum is feasible by the BP and BAs monolayer when the biaxial strain is incorporated. These results elucidate a promising way to manipulate the optical and electronic properties of monolayer BP and BAs via strain engineering and eventually make these materials promising for futuristic spintronics, electronics, and optoelectronic device applications.