The 21-year-old made his Premier League debut earlier this season, filling in when Tim Krul and Rob Elliot were sidelined with injury.
Bantams manager Phil Parkinson told the club's website: "Some of the top Premier League sides have five and six goalkeepers on their books but some of them have no real experience at all. We needed someone who had already enjoyed a taste of first-team football."
The stopper added: "This is a great club to move to and I can't wait to get started here and hopefully play some games.
"As a club, Bradford still have plenty to play for this season and I'm coming here to try and help win as many points as possible for the team."
Anwick's brother, Ben Alnwick, also plays in League One for Peterborough United.