Wood, 25, scored 30 times in 48 appearances for Leeds last season, and leaves Elland Road having managed 44 goals in 86 appearances for the Whites in all competitions.
"Burnley football club is delighted to confirm the signing of striker Chris Wood from Leeds United for a club-record fee," read a statement on the Premier League club's official website.
"The New Zealand international joins the Clarets on a four-year deal to become manager Sean Dyche's sixth new signing of the summer transfer window."
Wood told Burnley's official channel: "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."
Wood, who has previously played in the Premier League for West Bromwich Albion and Leicester City, will wear the number 11 shirt for his new club.