Drury, 35, has signed with City on loan until 5 April 2014.
Subject to receiving the necessary F.A and Football League clearances, Drury will now go into contention for the Bantams' match with Brentford this Saturday at Griffin Park.
Drury will wear squad number 6 during his time at the Coral Windows Stadium.
The Cottenham-born defender's presence in the City squad will now help to improve the options available Parkinson on the left hand side of the Bantams' defence.
The experienced defender joined Leeds in 2012 after an eleven-year spell with Norwich City.
During his time at Carrow Road, Drury won Norwich's Player of the Year award and enjoyed a spell playing Premiership football.
Despite his long association with Norwich, Drury actually started his career at Peterborough United. He spent six years at London Road before his move to the Canaries back in 2001.
Drury has won promotion three times during his career - once with Peterborough and twice following his move to Norwich.