Brady started his career with his local junior side Renton Thistle before moving to Newcastle West End.

[3][a] In August 1889 Brady had been convinced to join Everton by their captain Andrew Hannah, also from Alec's hometown of Renton.

After scoring twice on his debut against Stoke and a hat-trick in the 11–2 against Derby in the FA Cup (Everton's record victory), they narrowly missed out on winning the league title to Preston North End.

[6] In the summer of 1891 he was lured back to Scotland along with Everton teammate Dan Doyle to play for Celtic in the second season of the Scottish Football League.

[9] He was a part of the Wednesday side that won the FA Cup in 1896, making Brady one of the first players to win both the Scottish and English trophies at a time when they were considered the pinnacle of football competitions.