Having learned to play drums in both high school and as part of his father's church, Brady initially sought out a career in business, focusing on the music industry. This led to A&R roles at several major record labels, before ultimately becoming manager to the Brand New Heavies. He has played as part of Emmylou Harris's band, Spyboy, Steve Earle and the Dukes, Dave Matthews & Friends, and with Buddy & Julie Miller as well as being one of the music industries most sought after session drummer.

Early 1995 saw Emmylou Harris persuade Brady to join her touring band Spyboy, along with Daniel Lanois and Darryl Johnson. The following year they were joined by Buddy Miller and toured throughout the mid-nineties, culminating in a live album Spyboy, released in 1998.

Touring the world with Emmylou Harris led Brady to encounter and be seen by some of the key figures in the American music scene which resulted in Brady becoming one of the most in-demand session drummers around. Brady took part in extensive tours and sessions with the Steve Earle during his El Corazón period; Jewel throughout her 1998 Spirit world tour; and the Indigo Girls on their 1999 album Come on Now Social, 2002's Become You, 2004's All That We Let In, and 2011's Beauty Queen Sister.

In recent years, Brady has expanded his work to include production and writing. His work has largely been focussed on working with new acts, developing their song-writing and ultimately producing and recording with them. He has had a number of major successes, particularly in Australia and New Zealand, where his work has featured prominently in their national music charts, producing the debut records of both Brooke Fraser and Annabel Fay and Annah Mac.

Throughout 2006 Brady toured with Scottish singer Freddie Stevenson across the USA and Europe, as well as featuring on the most recent Solomon Burke record Nashville, and on the latest Waterboys record Book of Lightning.

In early 2013, Brady gathered several musicians, including Jakob Dylan, Dave Matthews, Charlie Sexton, and Sexton's brother Will, to his studio in Shreveport to record. This jam session eventually led to the formation of a band called The Nauts with Blade, Dylan, Matthews, and the Sexton brothers as members. 

In summer 2014, Brady appeared on Late Show with David Letterman as a drummer, performing alongside artist John Doe.