The ex-Leeds Rhinos and Castleford Tigers star joins with immediate effect and has agreed a deal until the end of 2018.
Gibson, 30, has played just six games for Wakefield this season, struggling to hold down a regular spot and spending time at both Dewsbury Rams and Oxford.
However, having played his entire career in Super League, a player of his calibre will be invaluable as bottom-placed Bradford seek to escape the drop from the Championship.
The ex-Salford Red Devils player, who can also play wing, has trained today and comes straight into the squad for Sunday’s derby at Halifax.
“My agent got on the phone to me last night,” said Leeds-born Gibson.
“We’ve been talking about it for a few days and last night the move came to life.
“It happened really fast; I got the contract emailed through and then came up to the club. I got my boots on straight away and got into training.
“I’ve been in Super League for a few years now, so I hope that I can bring some of my experience to the side.
“It’s something that I’m really looking forward to and hope we can kick on.”
Bulls coach Geoff Toovey said: “We don’t have to train him; he can step straight in and carry on from where he left off.
“A person of his quality and experience can step right in.
“He trained with us today, he felt at home and didn’t miss a beat really.
“I’m sure he’ll be well regarded by the fans and fellow players.
“I’m sure that he will help enhance and bring some tenacity to the club when things get tough in a game.
“The Bradford club is a place where people want to play - it has a lot of history and status in the game - so I’m not surprised but I’m very grateful and hopefully he can help us finish the year strongly.”