A statement on Bradford's website said: "The deal can and will be extended should both parties feel happy with proceedings between now and the conclusion of the current campaign.
"The board will, however, also still exercise the option of holding interviews with other potential applicants during that period should they see fit."
Taylor, whose former clubs include Leicester, Hull and Crystal Palace as well as a match in charge of the senior England side in which he made David Beckham the national captain, will be introduced to the squad on Wednesday morning and take control for Saturday's trip to Accrington.
It will be his first game since being dismissed as manager of Wycombe in October.
Bradford are 17th in League Two, 12 points off the play-off places, following Saturday's goalless draw with Grimsby.
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