Burnley have reportedly paid £15m and the New Zealand international, who becomes the sixth new arrival at Turf Moor this summer, has put pen-to-paper on a four-year, keeping him at the club until 2021.
Speaking about his move, the 25-year-old told Clarets Player HD: "My ambition has been to play in the Premier League for years. 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."
Wood could make his debut in Wednesday night's second-round tie at Blackburn Rovers or manager Sean Dyche may decide to leave the striker until the weekend when the Clarets travel to Wembley to take on Tottenham Hotspur.