A cascaded control structure is proposed in this paper for injecting active and reactive power in a three-phase grid-connected solar photovoltaic (PV) system by considering external disturbances. In the proposed cascaded control structure, there are two control loops—the outer loop voltage controller is used to ensure a continuous balance in power flow between the PV arrays and electrical power grid whereas the inner loop current controller controls the output current of the inverter. Moreover, the DC-DC boost converter is controlled to achieve a constant voltage at the input of the inverter. In order to obtain the power balance and extract maximum power, an incremental conductance (IC) based maximum power point tracking (MPPT) method is used in this paper. The current controller is designed using a nonlinear adaptive backstepping technique to regulate the active and reactive components of the grid current. The regulation of these currents towards desired values which in turn control the active and reactive power delivered into the grid. The overall stability analysis of the system is performed based on the formulation of control Lyapunov functions (CLFs). Finally, the performance of the designed controller is tested on three-phase grid-connected PV systems with single as well as multiple PV units under different environmental conditions and compared with an existing sliding mode controller. Simulation results confirm the effectiveness of the proposed adaptive backstepping control scheme and demonstrate the superior performance over the sliding mode controller.