Brady started his career at Arsenal, moving to London in 1971, at the age of 15. He turned professional on his 17th birthday in 1973, and made his debut on 6 October 1973 against Birmingham and put in an assured performance. In 1974–75, Brady was a first-team regular at Arsenal, and shone as a rare light in a side that hovered close to relegation for a couple of seasons in the mid-1970s. Arsenal won the 1979 FA Cup final against Manchester United, with Brady starting the move that ended in Alan Sunderland's famous last-minute winner. During his time he was voted the club's player of the year three times, and chosen as the PFA Player of the Year in 1979. In 1980, he featured in the Cup Winners' Cup final losing to Valencia on penalties.