Jones, 22, has penned a two-and-a-half year deal which will keep him at the Northern Commercials Stadium until the end of the 2018/2019 season.
City have fought off strong competition for the exciting forward, who has already netted ten goals in Sky Bet League One this season in a twenty-one game loan spell with Port Vale during the first half of the campaign.
The 6' 0'' attacker has certainly caught the eye of many in recent months after a number of well-taken goals, including smart finishes against promotion hopefuls Peterborough United, Scunthorpe United and Millwall.
Subject to receiving the relevant clearances, the new Bantams striker could be in line to make up part of City boss Stuart McCall's match-day squad for Saturday's home game with Chesterfield.
Speaking about the move, Jones said: "As soon as I knew a team the size of Bradford were interested in me, I was always drawn to them more than the others interested in me.
"I am delighted that I have been given the opportunity to come here and hopefully I can repay their faith with some goals.
"I love to try and score goals, that is what my game is all about. I try to get into scoring positions and cause defenders problems.
"I wasn't on loan at Port Vale when they played here (Bradford City) but the lads there told me what a tough game it was for them.
"It was good to get out on loan and get some first team experience, and I think I've taken my chance and managed to get this move to Bradford.
"Having spoken to the club prior to signing, they were all about nurturing young players my age.
"That really stuck out for me - I hope that I can come here and improve as a player and help improve the club."
Born in Sutton Coldfield, Jones started his professional career with West Bromwich Albion after coming through the youth ranks at the Hawthorns.
Jones moved to neighbours Birmingham in 2015. During his time at St Andrews, Jones also enjoyed a brief loan spell with Grimsby Town before his period with Vale.
City supporters can see Alex's first video interview as a Bantam by clicking on the screen below.