The 23-year-old, who scored six goals in 39 appearances last season has been the subject of much speculation over the summer, and it has now been confirmed that he will join Rovers ahead of the 2017/18 Sky Bet League One campaign.
Dack joined the club as an under-15 and impressed heavily during the 2011/12 season when he scored over 30 goals for the youth team.
Following the appointment of Martin Allen as Manager, Dack started to assert himself as a first team regular, making his debut away at Bristol City in the first round of the League Cup before scoring his first goal in a 3-2 defeat away at Crawley in the EFL Trophy.
Gillingham went on to win the League Two title with Dack himself appearing on 24 occasions in all competitions.
Dack continued to make solid progress; his goal against Sheffield United on the opening day of the 2015/16 season was a sign of things to come, and after consistently strong performances he was voted the League One Player of the Year at the end of the campaign as Gills fell just short of booking a play-off position.
His last goal for the club came in a 2-1 win over Bury at Gigg Lane in March. In total Dack made 185 appearances for the Gills and scored 38 goals.
The attacking midfielder will welcome his former team-mates to Ewood Park on Saturday September 30, before making his return to MEMS Priestfield Stadium on Saturday March 17.
Chairman Paul Scally said: “As much as we’re disappointed to see Bradley go we understood that he needed a fresh challenge to further his career.
“He’s been a fantastic servant to Gillingham Football Club and we wish him every success for the future.”