The former Huddersfield Town player, 31, who spent five seasons at Deepdale, can play at left-back and right-back and will provide manager David Hopkin with a senior option and versatility in his backline.
Woods has featured just twice for North End this season, coming on as a substitute in the New Year's Day loss at Rotherham United and starting in the EFL Cup game with Morecambe in August.
Woods said: "As soon as I knew Bradford were interested, I wanted to come and play.
"I have played in this league before, as well as having enjoyed a few promotions into the Championship, so will bring some experience with me.
"Bradford is a massive club and everybody knows that. We are not where we want to be at the minute but, hopefully, we can start to push ourselves up the table."
Swedish defender Thomas Isherwood has left Valley Parade by mutual consent after agreeing an early release to his deal, the club have confirmed.