Please see the following paper with many helpful refs (https://www.nature.com/articles/nrd1468). Since it is behind a paywall, here's the relevant bit...

"Pfizer was seeking a drug for angina when it originally created sildenafil (Viagra) in the 1980s. As an inhibitor of phosphodiesterase-5 (PDE5), sildenafil was intended to relax coronary arteries and therefore allow greater coronary blood flow. The desired cardiovascular effects were not observed on the healthy volunteers tested at the Sandwich, England, R&D facility in 1991–1992. However, several volunteers reported in their questionnaires that they had had unusually strong and persistent erections. Pfizer researchers did not immediately realize that they had a blockbuster on their hands, but when a member of the team read a report that identified PDE5 as a key enzyme in the biochemical pathway mediating erections, a trial in impotent men was quickly set up. A large-scale study carried out on 3,700 men worldwide with erectile dysfunction between 1993 and 1995 confirmed that it was effective in 63% of men tested with the lowest dose level and in 82% of men tested with the highest dose. Of note, in many of these studies, Pfizer’s researchers had difficulties retrieving unused sample of the drug from many subjects in the experimental group as they did not want to give the pills back! By 2003, sildenafil had annual sales of US $1.88 billion and nearly 8 million men were taking sildenafil in the United States alone."

Sildenafil was approved for ED in the US in 1998, but was later approved for pulmonary hypertension in the US 2005.