Wood started his senior career with Cambridge, Waikato and Hamilton Wanderers before moving to England to play for Premier League club West Bromwich Albion.

After a loan spell with Ipswich Town in 2015, he signed for Championship club Leeds United where he became the top scorer in the 2016–17 season, with 27 goals.

Wood then joined Burnley for a club record fee, and became a consistent goalscorer for them in the Premier League, notching up 49 goals in 144 matches over four and a half seasons.

[6] Wood began his footballing career at Onehunga Sports; after moving to Hamilton aged 11, he attended St Paul's Collegiate School.

[12] He found a rich vein of goal scoring form for West Brom's youth academy side, leading to a call-up to the reserve team where he was just as prolific.

[13] Injuries to several West Brom players saw Wood handed a surprise call up to the first-team for a Premier League match against Portsmouth at Fratton Park in April 2009.

[16] He scored his first professional goal for West Brom on 15 September 2009, a "stunning" 25-yard strike into the top left corner, in a 3–1 win over Doncaster Rovers.

[25] Playing as the lone striker in Birmingham's first match in major European competition for nearly 50 years, the Europa League play-off round first leg against Portuguese club Nacional, Wood hit the frame of the goal twice.

[31] Four days later, Wood scored in the 10th minute of stoppage time to defeat Club Brugge 2–1 in the Europa League group stage.

[39] He made his Millwall debut as a substitute for Darius Henderson against Cardiff City, and on his first start, scored a consolation goal against his former club Brighton & Hove Albion.

[44] Wood started and scored twice after only 24 minutes in his first game for Leicester on 1 January 2013 against Huddersfield Town, initially joining on loan to be registered in time to play.

[47] Five days later, after replacing Jamie Vardy as a substitute, Wood scored a "stunning" long-range volley against Burnley to put Leicester six points clear at the top of the Championship.

[53] On 1 July 2015, Wood joined Championship club Leeds United on a four-year contract for an undisclosed fee,[54][55] reported to be in the range of £2.5–3 million.

[62] His ninth goal of the season came in extra time of the League Cup fourth-round tie against Norwich to make the score 2–2, and he converted his kick as Leeds won in a penalty shoot-out.

[76] On 21 August 2017, Wood signed a four-year contract with Premier League club Burnley for an undisclosed club-record fee,[77] widely reported as £15 million.

[78] Wood made his Burnley debut on 27 August against Tottenham Hotspur at Wembley Stadium in the Premier League, and scored an equaliser in the second minute of stoppage time in a match which finished 1–1.

[79] On 19 September, in the EFL Cup third round, Wood scored against his former club Leeds United at Turf Moor in the 89th minute from the penalty spot.

[84] On 13 January 2022, Wood signed a two-and-a-half-year contract with Newcastle United for a fee reported to be £25 million, after his release clause was triggered.

[87] He made his Newcastle debut two days after signing when he started in a 1–1 draw against Watford,[88] and his first goal for the club was the equaliser in a 2–1 league win over Southampton on 10 March.

[89] Wood found his first-team chances at Newcastle limited, and on 20 January 2023, he joined Premier League club Nottingham Forest on loan to the end of the season.

[95] Later that year, on 26 December, he scored a hat-trick in a 3–1 away victory over Newcastle United,[96] becoming only the fourth player in Premier League history to achieve this feat against his former club following Andy Cole, Marcus Bent and Joshua King.

[99] On 7 December 2024, he became Forest's top leading goalscorer in the Premier League, bypassing Bryan Roy, as he netted the winner in a 3–2 away victory over Manchester United.

[101] On 1 February, he netted a hat-trick, the third goal of which was a penalty, in a 7–0 victory over Brighton, becoming the first Nottingham Forest player to achieve this feat at the City Ground in the top flight since Nigel Clough in December 1987.

[102] Wood represented New Zealand at under-17 level and was a standout performer for the All Whites at the 2007 FIFA U-17 World Cup,[103] a tournament which earned him a trial with West Brom, for whom he later signed.

[12] After a string of impressive performances at club level, Wood's rise on the international stage continued as he was fast-tracked into All Whites coach Ricki Herbert's squad for the 2009 FIFA Confederations Cup in South Africa.