This paper proposes a Model Predictive Control (MPC) framework for designing a guidance and control (G&C) system for multi-satellite assembly in proximity operation. The control system is designed by using a linear time-invariant dynamic model for circular orbit (Hill-Clohessy-Wiltshire model). Output and input constraints are studied and implemented in linear form to reduce the computational power. A collision-free maneuver is ensured by setting a hyper-plane-rotation constraint. In addition, a new form of line-of-sight constraint is developed based on the first-order approximation of the circular cone equation to guarantee smooth docking. Moreover, control input constraints are considered by setting upper and lower bounds for each input. The robustness of the system is studied by simulating the response for elliptical orbit with different values of eccentricity. The proposed GNC is verified in three stages; first, numerical simulation has been performed, second, optimized C++ code is generated and its results are compared to simulation results, and third, the C++ code is tested on the target board to verify the ability to compute the control action within the sampling time.