Millimeter-wave (mmWave) bands have deservedly taken their place in the development of next-generation network communications to address the explosive growth of mobile net- work data traffic and high-speed communications requirements. Also, the fully connected hybrid architecture can offer a suitable beamforming gain for overcoming the limitations of mmWave sig- nals in outdoor communications. Consequently, for the feasibility of the hybrid architecture implementation, the designing of the optimal analog/digital beamformers is indispensable for provid- ing good performance with the lowest complexity. Therefore, in this work, we develop a low-complexity alternating minimization design using a complete closed-form least-square method in the iterative design process to derive the optimal analog and digital beamformers by considering the total power constraint at the transmitter and the unit constant modulus constraints. Thanks to the offered global optimal solutions and the fast convergence of the least squares method, numerical results demonstrated that the proposed design attains perfect performance with the lowest computational complexity compared to the state-of-art design algorithms in terms of spectral efficiency (SE) in different scenarios.