We report the electronic structure, optical and charge transport properties of the unexplored ternary Zintl phases KCuX(X=Se,Te) from the first principles calculations employing the full-potential linearized augmented plane-wave (FLAPW) method with the Tran Blaha modified Becke-Johnson (TBmBJ) potential. It is demonstrated that the materials are direct band gap (1.13, 1.38 eV) semiconductors with covalent bonding between Cu and (Se/Te). The calculated low effective mass and high carrier mobility (over 105 cm2/V.s) accentuate that KCuX have good carrier transport and the materials may have possible applications in solar cell absorbers and nanoelectronic devices. Absorption spectra indicates that the ternary crystals are UV-A light absorbers and could be useful in photovoltaic and photodetector applications. A study on the effect of pressure (till 5 GPa) is carried out in order to further explore the materials for their electronic band gaps and charge transport properties as they are proposed to be useful in future contemporary electronic devices. It is observed that pressure enhances the intrinsic carrier mobility and thermal stability of KCuX, indicating that the materials can withstand robust external conditions.