Clarke, 31, has penned a one-year deal at the Coral Windows Stadium with the option for a further year.
He is now due to feature in this Tuesday night's friendly at Whitby Town.
The defender has joined City on a free transfer after officially leaving previous club Leyton Orient on Monday.
The former Orient captain was in the crowd at the Coral Windows Stadium to watch City's victory over Carlisle United last Saturday.
After completing his move to City, Clarke said: "Having played against a lot of the players here, I know they are a great bunch of lads. I just can't wait to get involved now.
"All of my career has been played at League 1 level so I hope I can bring that experience to the team.
"Playing for Huddersfield previously and being from this area, I know the size of Bradford already.
"The support the club gets and the size of the stadium - I'm just glad I'm part of it now."
Clarke made 131 appearances for Orient having joined the London-based club in 2012.
One of the main highlights of Clarke's Orient career came when he led them to the Sky Bet League 1 Play-Off final against Rotherham United back in May 2014.
The defender's move to the Coral Windows Stadium will see him return to West Yorkshire having begun his career at Huddersfield Town.
Born in Halifax, Clarke made his professional debut for Huddersfield in September 2001, aged only 17, after coming through the Terriers' youth ranks.
Clarke made exactly 300 appearances for Huddersfield, twice playing in the League 1 Play-Off semi-finals (2006, 2010) for the Terriers.
He also enjoyed loan spells with Colchester United, Oldham Athletic and Bury during his eleven-year pro career at Huddersfield.
Along with his commendable defensive qualities, Clarke also possesses a huge long throw-in that can be utilised at attacking set-pieces.
Clarke's younger brother Tom, currently a professional footballer himself at Preston North End, enjoyed a brief loan spell with the Bantams in 2008.