The responsibility had been held by Danny Murphy ever since he joined the club last summer on a free transfer from Premier League outfit Fulham.
However, the experienced midfielder has not featured on a regular basis under new manager Michael Appleton, who has now decided that centre-back Dann is the player to lead his team.
"It was a difficult decision to make but I think it is one that is going to benefit everyone," Appleton told reporters.
"Danny took it very professionally as I expected him to do. He's an experienced player, these things happen, and you have to make these decisions sometimes.
"Moving forward I think it is going to be the best thing for the football club as a whole. Scott is someone who leads by example and I think his two performances since he took over the role have been magnificent."
Dann signed for Rovers in 2011 following a stint with Birmingham City.