Clarke made 35 appearances for City after joining the club back in July 2015, helping the Bantams into the Sky Bet League One Play-Offs at the end of last season.
The 33 year-old left Valley Parade to join fellow League One side Coventry City last weekend, with Clarke making his Sky Blues debut against Bolton Wanderers on Monday.
In a statement aimed towards the Bantams faithful, the centre half said: "I would like to thank everybody associated with Bradford City Football Club.
"My short time at the club has been a fantastic experience and I have met some great people.
"The support of the fans has shown what a great club this is, and I would like to thank you all and wish only the best for the club.
"All the very best for the rest of the season."