Wood, 25, signed a four-year contract at Turf Moor on Monday to become the club's sixth signing of the transfer window.
The New Zealand international is in contention to make his debut in Wednesday's EFL Cup derby against rivals Blackburn Rovers.
"My ambition has been to play in the Premier League for years," Wood told his new club's 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 is 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."
Wood will wear the number 11 shirt at Burnley and arrives after Sean Dyche's men sold last season's first-choice striker Andre Gray to Watford in a reported £18.5m deal earlier this month.
He spent two years at Leeds, impressing with 27 Championship goals last season, and thanked the club in a statement after sealing his move.
Leeds Utd pic.twitter.com/7bohbbuwSc— Chris Wood (@officialcwood) August 21, 2017
Leeds chairman Andrea Radrizzani revealed the club tried to negotiate a new three-year deal with Wood, but felt he had to sell to when Wood made it clear he wanted to leave for the top flight, as there was only one year remaining on his existing contract.