Background: An adverse drug event (ADE) is commonly defined as "an injury resulting from medical intervention related to a drug."Providing information related to ADEs and alerting caregivers at the point of care can reduce the risk of prescription and diagnostic errors and improve health outcomes. ADEs captured in structured data in electronic health records (EHRs) as either coded problems or allergies are often incomplete, leading to underreporting. Therefore, it is important to develop capabilities to process unstructured EHR data in the form of clinical notes, which contain a richer documentation of a patient's ADE. Several natural language processing (NLP) systems have been proposed to automatically extract information related to ADEs. However, the results from these systems showed that significant improvement is still required for the automatic extraction of ADEs from clinical notes. Objective: This study aims to improve the automatic extraction of ADEs and related information such as drugs, their attributes, and reason for administration from the clinical notes of patients. Methods: This research was conducted using discharge summaries from the Medical Information Mart for Intensive Care III (MIMIC-III) database obtained through the 2018 National NLP Clinical Challenges (n2c2) annotated with drugs, drug attributes (ie, strength, form, frequency, route, dosage, duration), ADEs, reasons, and relations between drugs and other entities. We developed a deep learning-based system for extracting these drug-centric concepts and relations simultaneously using a joint method enhanced with contextualized embeddings, a position-attention mechanism, and knowledge representations. The joint method generated different sentence representations for each drug, which were then used to extract related concepts and relations simultaneously. Contextualized representations trained on the MIMIC-III database were used to capture context-sensitive meanings of words. The position-attention mechanism amplified the benefits of the joint method by generating sentence representations that capture long-distance relations. Knowledge representations were obtained from graph embeddings created using the US Food and Drug Administration Adverse Event Reporting System database to improve relation extraction, especially when contextual clues were insufficient. Results: Our system achieved new state-of-the-art results on the n2c2 data set, with significant improvements in recognizing crucial drug-reason (F1=0.650 versus F1=0.579) and drug-ADE (F1=0.490 versus F1=0.476) relations. Conclusions: This study presents a system for extracting drug-centric concepts and relations that outperformed current state-of-the-art results and shows that contextualized embeddings, position-attention mechanisms, and knowledge graph embeddings effectively improve deep learning-based concepts and relation extraction. This study demonstrates the potential for deep learning-based methods to help extract real-world evidence from unstructured patient data for drug safety surveillance.