As part of the large number of scientific articles being published every year, the publication rate of biomedical literature has been increasing. Consequently, there has been considerable effort to harness and summarize the massive amount of biomedical research articles. While transformer-based encoder-decoder models in a vanilla source document-to-summary setting have been extensively studied for abstractive summarization in different domains, their major limitations continue to be entity hallucination (a phenomenon where generated summaries constitute entities not related to or present in source article(s)) and factual inconsistency. This problem is exacerbated in a biomedical setting where named entities and their semantics (which can be captured through a knowledge base) constitute the essence of an article. The use of named entities and facts mined from background knowledge bases pertaining to the named entities to guide abstractive summarization has not been studied in biomedical article summarization literature. In this paper, we propose an entity-driven fact-aware framework for training end-to-end transformer-based encoder-decoder models for abstractive summarization of biomedical articles. We call the proposed approach, whose building block is a transformer-based model, EFAS, Entity-driven Fact-aware Abstractive Summarization. We conduct experiments using five state-of-the-art transformer-based models (two of which are specifically designed for long document summarization) and demonstrate that injecting knowledge into the training/inference phase of these models enables the models to achieve significantly better performance than the standard source document-to-summary setting in terms of entity-level factual accuracy, N-gram novelty, and semantic equivalence while performing comparably on ROUGE metrics. The proposed approach is evaluated on ICD-11-Summ-1000, and PubMed-50k.