Sky Sports says Wood has cost the Premier League side £15million and he could make his debut in their local derby against Blackburn on Wednesday in the second round of the Carabao Cup.
The New Zealand striker rose to prominence by finishing as the Sky Bet Championship's leading scorer with 27 goals last season and will now get his chance to shine in the top-flight under Sean Dyche.
"My ambition has been to play in the Premier League for years," Wood, who has signed a four-year deal, told Clarets Player HD.
"I've had tastes of being in there but I've never had the chance to give it a proper bash.
"Coming here I feel I've got a proper opportunity to do that. I've never started a Premier League game and this what I want to do.
"This is a club that wants to stay in the Premier League for years to come and it's going that way.
"The squad has done fantastically over the last couple of years to put themselves in the position they are now.
"There have been some great additions this summer, which I'm sure has given everyone an added boost, to move forward and cement us as a Premier League team and looking on further up the league.
"The manager has given me a lot of confidence and backed me to bring me here, which is what you want.
"I've still got a lot of good years ahead of me. I've got lots of ambitions to achieve in the future. I've got goals and dreams that I want to achieve and it starts here."