The 31-year-old keeper had his contract at Town cancelled by mutual consent which has allowed him to sign a contract with The Bantams which will run until the end of the season.
Two weeks ago fellow Town keeper Simon Eastwood returned early from what was expected to be a season long loan deal with Bradford.
"We're delighted to bring Matt to the club, he's a goalkeeper with a great pedigree and a good track record," City boss Stuart McCall has said.
"He brings lots of experience with him, which is exactly what we were after, and he is also very vocal and a good talker, which is important.
"Once it became clear that Easty was going back, Matt was our number one target.
"We have had a lot of goalkeepers put to us over the last few weeks, but Matt fits the bill perfectly."