Pressman, 44, was sacked along with manager Ian Baraclough in March 11 as the Iron crashed towards relegation from the Championship.
He returned to football that August when he moved to Valley Parade as goalkeeper coach, and has now taken on the same role at the Lions.
"It is a shame to see Kev leave the football club but he goes with our best wishes," said Bradford boss Phil Parkinson.
"We wish him all the best in his new career move and we now focus on naming his replacement in plenty of time for the new season."