Brady was selected by NASA in March 1992 and reported to the Johnson Space Center in August 1992. He was qualified for selection as a Mission Specialist on future Space Shuttle flight crews. Technical assignments included: working technical issues for the Astronaut Office Mission Development Branch; flight software testing in the Shuttle Avionics Integration Laboratory (SAIL); astronaut representative to the Human Research Policy and Procedures Committee; deputy chief for Space Shuttle astronaut training; and chief for Space Station astronaut training in the Mission Operations Division. He flew on STS-78 in 1996 and logged over 405 hours, more than 16 days, in space.