The 23-year-old, who is Bradford manager Phil Parkinson's fifth summer signing, has agreed a one-year deal at Valley Parade.
Atkinson, who spent the final four months of last season on loan with the Bantams, told the club's official website: "I'm obviously pleased to have this move all sorted before the new season."
He added: "I can now concentrate fully on having a good pre-season and getting ready for the year again. Knowing most of the players and staff from last season will certainly be an advantage. That can only help me going into the new season.
"I don't think I did as well as I could of done here last year. I was a little disappointed with my own performances. It was probably a little tough for me to come straight into a side that was struggling for wins a bit. I definitely have a lot more to give.
Beverley-born Atkinson, who started out as a trainee at the Tigers in 2007, has had loan spells at Port Vale, Mansfield, Rochdale, Rotherham and Plymouth. He made 12 appearances for Parkinson's side last season.