A fundamental drawback of the orthogonal frequency division multiplexing (OFDM), both in communication and radar, is its sensitivity to the Doppler effect. In this paper, we present a novel signal processing approach for OFDM radar and communication systems that overcomes the Doppler sensitivity of OFDM. We propose a scenario independent Doppler correction method that enables an intercarrier-interference free processing for OFDM. The Doppler robustness of the proposed approach opens new perspectives for system parameterization, enabling radar concepts not feasible before. We show in simulations that the proposed Doppler correction method is superior to the classical signal processing in many important aspects. Measurements with an OFDM-MIMO radar prototype are used to validate the proposed approach and to show its effectiveness in real-life applications.