The Lancashire club dropped down to the Championship at the end of last season and Appleton has become the outfit's third manager since.
"The owners are very, very ambitious," Appleton said in a press conference. "They want to get back into the Premier League and I still believe there is an opportunity.
"An opportunity to work at a club that I think and believe is a Premier League club was too good to turn down. I spoke to the owners and they convinced me about their ambition."
Appleton spent just 65 days in charge of Blackpool before switching to Ewood Park.