This paper presents a modal analysis‐based impact analysis of the change in system inertia due to the integration of the large‐scale doubly fed induction generator (DFIG)‐based wind turbine system (WTS) on the power system damping in inter‐area oscillation modes. The impact of replacement of a synchronous generator by WTS of same MVA capacity on system dynamics such as emergence of new critical modes of inter‐area oscillations affecting system stability is studied. Further, a double‐channel scheme‐based wide‐area damping controller (WADC) is proposed for WTS, which provides sufficient damping of prominent oscillation modes and enhanced stability margin to alleviate the negative impact of reduction in system inertia. The comparative assessment of the proposed controller with a PSS‐based WADC on a modified New England 10‐machine system validates the performance and is found to be more effective in mitigating inter‐area oscillation in the system. The real‐time feasibility of the proposed double‐channel WADC is evaluated on the Real‐Time Digital Simulator (RTDS) platform. The simulation results show that the proposed WADC can successfully mitigate various inter‐area modes simultaneously. Furthermore, it provides robust performance for a variety of contingencies, time delays in feedback signals, and uncertainties associated with different operating scenarios of WTS.