Appleton joined Rovers on a two-and-a-half year deal on 11 January after spending barely two months in charge of Blackpool.
Blackburn sit 13th in the Championship table, seven points of the play-off places, but Appleton insists he can guide them back to the top-flight.
"After having a conversation with the owners, they made it very clear that they have a burning desire and ambition to get back up to the Premier League as quickly as they possibly could," Appleton told the club's official website.
"I want to be part of that, they pretty much want me to make sure that I'm the driving force behind everything that they want in terms of their ambition. I just felt it was a footballing opportunity that I couldn't turn down.
"I want to be part of something that gets it back up where it belongs in the Premier League.
"I genuinely do believe (we can achieve) that with the right people and the right players, and certainly we've got some fantastic supporters.
"If we can get that balance right and get them back in and all pulling in the same direction, I genuinely believe that will happen."
Appleton also has two new members of his backroom staff sorted out with goalkeeping coach John Keeley and recruitment guru Luke Dowling joining him from Portsmouth.