Abstract Objective To develop a natural language processing system that solves both clinical concept extraction and relation extraction in a unified prompt-based machine reading comprehension (MRC) architecture with good generalizability for cross-institution applications. Methods We formulate both clinical concept extraction and relation extraction using a unified prompt-based MRC architecture and explore state-of-the-art transformer models. We compare our MRC models with existing deep learning models for concept extraction and end-to-end relation extraction using 2 benchmark datasets developed by the 2018 National NLP Clinical Challenges (n2c2) challenge (medications and adverse drug events) and the 2022 n2c2 challenge (relations of social determinants of health [SDoH]). We also evaluate the transfer learning ability of the proposed MRC models in a cross-institution setting. We perform error analyses and examine how different prompting strategies affect the performance of MRC models. Results and Conclusion The proposed MRC models achieve state-of-the-art performance for clinical concept and relation extraction on the 2 benchmark datasets, outperforming previous non-MRC transformer models. GatorTron-MRC achieves the best strict and lenient F1-scores for concept extraction, outperforming previous deep learning models on the 2 datasets by 1%–3% and 0.7%–1.3%, respectively. For end-to-end relation extraction, GatorTron-MRC and BERT-MIMIC-MRC achieve the best F1-scores, outperforming previous deep learning models by 0.9%–2.4% and 10%–11%, respectively. For cross-institution evaluation, GatorTron-MRC outperforms traditional GatorTron by 6.4% and 16% for the 2 datasets, respectively. The proposed method is better at handling nested/overlapped concepts, extracting relations, and has good portability for cross-institute applications. Our clinical MRC package is publicly available at https://github.com/uf-hobi-informatics-lab/ClinicalTransformerMRC.