Colorectal cancer (CRC) is one of the most common causes of cancer and cancer-related mortality worldwide. Performing colon cancer screening in a timely fashion is the key to early detection. Colonoscopy is the primary modality used to diagnose colon cancer. However, the miss rate of polyps, adenomas and advanced adenomas remains significantly high. Early detection of polyps at the precancerous stage can help reduce the mortality rate and the economic burden associated with colorectal cancer. Deep learning-based computer-aided diagnosis (CADx) system may help gastroenterologists to identify polyps that may otherwise be missed, thereby improving the polyp detection rate. Additionally, CADx system could prove to be a cost-effective system that improves long-term colorectal cancer prevention. In this study, we proposed a deep learning-based architecture for automatic polyp segmentation called Transformer ResU-Net (TransResU-Net). Our proposed architecture is built upon residual blocks with ResNet-50 as the backbone and takes advantage of the transformer self-attention mechanism as well as dilated convolution(s). Our experimental results on two publicly available polyp segmentation benchmark datasets showed that TransResU-Net obtained a highly promising dice score and a real-time speed. With high efficacy in our performance metrics, we concluded that TransResU-Net could be a strong benchmark for building a real-time polyp detection system for the early diagnosis, treatment, and prevention of colorectal cancer. The source code of the proposed TransResU-Net is publicly available at https://github.com/nikhilroxtomar/TransResUNet.