Morris, 23, has penned a three-year deal with City after negotiating his departure from the Championship side.
The Preston-born player will move from Ewood Park to the Coral Windows Stadium on a free transfer although Blackburn have included a sell-on fee into the deal.
Morris, who joined up with his new City team-mates at training for the first time this week, can play either on the left wing or in more of a central midfield role.
Previous to his move to the Bantams, Morris spent the last year and a half on loan with Fleetwood Town, helping them to win the League 2 Play-Off Final back in 2014.
Morris also netted an impressive eight times from midfield during Fleetwood's first ever campaign in League 1 last season. His tally for the 2014/2015 campaign made him Fleetwood's joint top scorer for the season.
Bantams boss Phil Parkinson said: "We are delighted to have Josh on board.
"We have tracked his progress for some time and he enjoyed a good season in League 1 with Fleetwood Town last year.
"He got eight goals from midfield for Fleetwood last season, making him one of their top scorers, and he will add something extra to the squad. We look forward to working with him."
Despite his recent links with Fleetwood, Morris has still managed to play over twenty times for Blackburn during his career in both the Premier League and Championship.
Before his time at Fleetwood, the former England Under 20 international also had loan spells with Rotherham United, Carlisle United and Yeovil Town.