The club said Brady was expected to work with its sports science department as well as the board and the management team on "global marketing efforts and the identification of new commercial partnership opportunities".
The retired NFL quarterback entered a partnership with Knighthead Capital Management to become a minority owner at the club which finished 17th in England's second tier last season.
"Tom Brady joining the Birmingham City team is a statement of intent. We are setting the bar at world class. Tom is both investing and committing his time and extensive expertise," chairman Tom Wagner said in a statement.
Brady described City, which last played in the top flight Premier League in 2011, as an "iconic club".
"I've been part of some amazing teams in my day, and I'm looking forward to applying my perspective to create that same success here in Birmingham," Brady said.
Brady has been busy off the pitch since his retirement. He was unveiled as the newest celebrity team owner in the E1 World Championship, the new electric race boat competition.
He also acquired an ownership stake in WNBA side Las Vegas Aces.
