This paper employes a nonlinear adaptive backstepping control scheme to design controllers for the machine-side converter (MSC) and grid-side converter (GSC) in permanent magnet synchronous generator (PMSG)-based wind farms. The controllers for the MSC and GSC are designed to ensure fault ride through (FRT) operations of wind farms. The proposed controllers are designed by considering full electrical dynamics of PMSG-based wind farms while considering all parameters associated with these dynamics as completely unknown. Parameter adaptation laws are used to dynamically estimate these unknown parameters and adaptation laws are also used to estimate the stator flux which eliminates the necessity of an additional observer. The control and parameters adaptation laws are designed in such a way the stability of the system is ensured under any circumstance. The FRT capability of the proposed scheme is tested through simulation studies on a grid-connected PMSG-based wind farm by applying a large three-phase short-circuit fault at the point of common coupling (PCC). Simulation results clearly shows that the proposed scheme provides adequate reactive power supports to ensure FRT operations as compared to a partial feedback linearizing controller (PFBLC).