Brady specialized in sports medicine and worked as team physician at several universities before joining the US Navy in 1986. There he became a flight surgeon, serving with the Blue Angels flight demonstration squad from 1988–1990. In 1992 he was selected for NASA's astronaut program and completed training to prepare for space flight. After serving in the astronaut program, he returned full-time to the Navy and served as flight surgeon at Whidbey Island Naval Air Station in the San Juan Islands before retiring in the Pacific Northwest.