Alnwick, 21, has signed on loan with City until the end of the regular 2014/2015 league season.
The Newcastle shot-stopper, who is the younger brother of Peterborough United 'keeper Ben Alnwick, has started in five of the Magpies' Premier League fixtures this season, including matches against Manchester United, Sunderland and Arsenal.
Following an injury to fellow 'keeper Rob Elliott, Alnwick also played the second half of Newcastle's league win over the previously unbeaten Chelsea last December.
On top of his six Premier League appearances this campaign, Alnwick has featured for Newcastle in the Capital One Cup and FA Cup as well.
Alnwick will wear squad number 1 following the recent return of Jordan Pickford back to Sunderland.
Subject to receiving the relevant clearances, Alnwick will now come into contention to make his City debut at Notts County on Saturday.
Given his participation in Newcastle's third round tie at Leicester City, however, Alnwick won't be allowed to play in the Bantams' FA Cup Quarter Final replay at Reading on Monday.
Bantams boss Phil Parkinson said: "It has been very hard to replace Jordan - no teams what to let 'keepers go out on loan at this time of year - so we are very grateful John Carver (Newcastle United manager) for letting us have Jak.
"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.
"We welcome Jak to the club and he adds competition for that goalkeeping spot."
Speaking about the move, Alnwick himself said: "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.
"I spoke with my brother (Ben Alnwick, Peterborough United) before this move and he said good things about this level. He trained here as well over the summer and he said Bradford is a brilliant club.
"To be honest though, I didn't need much convincing at all to come here. This is a big club with a massive fan-base and I've known of Bradford for many years now really. I am really excited by this move.
"The matches will come thick and fast here between now and the end of the season but I need games as much as possible."