Brady was signed as an undrafted free agent by the Dallas Cowboys after the 1987 NFL draft on April 1, who were looking for a replacement for kicker Rafael Septien.
[4] On September 22, 1988, he was signed as a free agent by the Indianapolis Colts to handle the kickoffs, while starter Dean Biasucci focused only on making field goals on the depth chart.
[5] On April 21, 1989, he was signed as a free agent by the Green Bay Packers to compete for the starting job against rookie Chris Jacke.
[6][7] On September 22, 1989, he was signed as a free agent by the Buffalo Bills to handle the kickoffs instead of Scott Norwood.
He currently lives in Long Beach, California and owns a medical device company manufacturing X-Ray aprons.