The 20-year-old arrives at the University of Bradford Stadium having been monitored by the club throughout the summer.
Born in Guernsey, Adams moved to the south of England as a youngster, signing for Eastleigh at under-16 level.
He made a permanent move to the DW Stadium in 2022, and spent the second half of the 2023/24 season on loan at Morecambe, where he made 21 appearances, finding the net on two occasions.
On joining the Bantams, he said: “I am buzzing to be here. I have waited quite a while over the summer and pre-season, but I am happy to be here now.
“I am really looking forward to starting, and am ready to make an impact here.”
City manager Graham Alexander added: “We have had to be patient waiting for Joe to join us, so we are very happy he is now here.
“His ability on the ball and running power will be a great addition to us.
“He is another player hungry to be successful, and I am sure his character and qualities will impress everyone.”
Adams spent the pre-season with Wigan, but an injury prevented him making a full case for a first team slot there.
Bradford are currently second in the Sky Bet League Two, keeping their unbeaten record with a 3-1 win against Bromley on the weekend.