The centre-back has worn the armband for Rovers' last two matches and his role will become permanent on Wednesday.
Dann will take over from former skipper Danny Murphy for the FA Cup replay with Millwall at Ewood Park.
Appleton said: "It was a difficult decision to make but I think it is one that is going to benefit everyone.
"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."