The New Zealand international, who has signed a four-year deal at Turf Moor, could make his debut as early as on Wednesday (23 August), when the Clarets travel to Ewood Park to face local rivals Blackburn Rovers in the second round of the Carabao Cup.
The 25-year-old joined Leeds in the summer of 2015 from Leicester City and went on to enjoy a successful spell at Elland Road, scoring 44 goals in 88 appearances, including 27 league goals last season as Leeds narrowly missed out on a playoff spot in the Championship.
"My ambition has been to play in the Premier League for years," he told Burnley's official website.
"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."
Wood's arrival means Burnley manager Sean Dyche has secured a like-for-like replacement for Andre Gray, who was sold to Watford earlier this month. Burnley kicked off the campaign with a surprising 3-2 win against Chelsea at Stamford Bridge but looked toothless as they fell to a 1-0 defeat against West Bromwich Albion over the weekend.
Finding the net has been a major problem for Dyche's men, who last season had the worst goalscoring record of all Premier League teams outside the bottom three.
However, having defied expectations last term, Burnley have bought shrewdly so far this summer, adding former Swansea City midfielder Jack Cork, while Jonathan Walters and Phil Bardsley arrived from Stoke City.
"This is a club that wants to stay in the Premier League for years to come and it's going that way," Wood added. "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."
Wood, who has scored 20 times in 52 appearances for New Zealand became the youngest captain of the 'All Whites' when he led the side for the first time in November 2014 and played in the 2010 World Cup in South Africa.