This paper deals with the control development of a wind energy conversion system (WECS) interfaced to a utility grid by using a doubly fed induction generator (DFIG), a back-to-back (B2B) converter and an RL filter for optimal power extraction. The aim was to design a sensorless controller to improve the system reliability and to simultaneously achieve the regulation of the generator speed, reactive power and DC-link voltage. The proposed global control scheme combines: (i) a high-gain observer employed to estimate the generator speed and the mechanical torque, usually regarded as accessible, (ii) a sensorless MPPT block developed to provide optimal generator speed reference, which is designed on the basis of the mechanical observer and a polynomial wind-speed estimator and (iii) a finite-time controller (FTC) applied to the B2B converter to meet the output reference’s tracking objectives in a short predefined finite time by using the backstepping and Lyapunov approaches. The proposed controller performance is formally analysed, and its capabilities are verified by numerical simulations using a 2 MW DFIG wind turbine (WT) under different operating conditions.