The 25-year-old moves to England’s top flight after finishing last season as the Championship’s top scorer with 27 goals.
In all he scored 44 goals in 88 appearances for Leeds.
The Clarets did not disclose the sum paid to Leeds but confirmed it was more than their previous record, around £13million for Robbie Brady from Norwich this year.
Wood, who joins on a four year deal, is Burnley manager Sean Dyche’s first signing of the transfer window.
Dyche — who has been keen on Wood as Andre Gray’s replacement since the latter left for Watford for a reported £18.5m earlier this month — said Wood would be one of several new recruits before the transfer window shuts at the end of the month.
“We are really happy to have Chris with us,” Dyche said at a press conference.
“He is 25, has a lot of goals in him and it is improving the competition and the quality of the group.
“Obviously some players have left us and I wanted to strengthen.
“He has only just got here, but we will see how he gets on over the next few days.
“We are in the market for a number of different positions.”
Wood returns to the Premier League after brief spells with West Bromwich Albion and Leicester City.
“My ambition has been to play in the Premier League for years,” Wood told the club’s 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.”
Auckland-born Wood has scored 20 times in 52 appearances for New Zealand.
He played in the 2010 World Cup as an 18-year-old, and went on to became the youngest captain of the ‘All Whites’ when he led the side for the first time in November, 2014.
He could make his debut for his new employers as early as Wednesday’s League Cup second round tie at Blackburn Rovers.
Burnley opened the new season upsetting champions Chelsea 3-2 before falling 1-0 to West Brom on Saturday.
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