Deep learning (DL) algorithms can enhance wireless communication system efficiency and address numerous physical layer challenges. Channel state estimation (CSE) and signal detection (SD) are essential parts of improving the performance of an OFDM wireless system. In this context, we introduce a DL model as an effective alternative for implicit CSE and SD over Rayleigh fading channels in the OFDM wireless system. The DL model is based on the gated recurrent unit (GRU) neural network. The proposed DL GRU model is trained offline using the received OFDM signals related to the transmitted data symbols and added pilot symbols as inputs. Then, it is implemented online to accurately and directly detect the transmitted data. The experimental results using the metric parameter of symbol error rate show that, the proposed DL GRU-based CSE/SD provides superior performance compared with the traditional least square and minimum mean square error estimation methods. Also, the trained DL GRU model exceeds the existing DL channel estimators. Moreover, it provides the highest CSE/SD quality with fewer pilots, short/null cyclic prefixes, and without prior knowledge of the channel statistics. As a result, the proposed DL GRU model is a promising solution for CSE/SD in OFDM wireless communication systems.