Born in Sydney, New South Wales, Brandt grew up in the Blue Mountains region. Living in his hometown of Springwood, he attended Blaxland High School in Blaxland, where he graduated from in 2007.
In 2008, Brandt moved to the United States to attend Lake Forest Academy in Lake Forest, Illinois for a prep season in 2008–09. In his one season playing for Lake Forest, he averaged 15 points and 10 rebounds per game for coach Matt Vaughn.
As a freshman at Oregon State in 2009–10, Brandt played sparingly for a Beavers team that finished the season with a 14–18 win/loss record. In 26 games (two starts), he averaged 1.1 points and 1.1 rebounds in 9.2 minutes per game.
As a sophomore in 2010–11, Brandt earned first-team Pac-12 All-Academic honors, while also earning a bigger role on the team which led to higher production value. In 29 games (21 starts), he averaged 4.8 points and 2.5 rebounds in 16.0 minutes per game.
As a junior in 2011–12, Brandt led the team in three-point field goal percentage with 49.2 percent (29-for-59), finished ninth in the Pac-12 in field goal percentage with 53.5 percent (122-for-228), and earned Pac-12 All-Academic Honorable Mention honors. In 36 games (35 starts), he averaged 9.1 points, 3.4 rebounds and 1.1 assists in 23.2 minutes per game.
On 16 November 2012, Brandt suffered an isolated tear of the ACL in his right knee against Purdue that required surgery and forced him to miss the remainder of the 2012–13 season. He was later granted medical hardship by the Pac-12 Faculty Athletics Representative Committee and deemed eligible to play in 2013–14. In four games (all starts), he averaged 11.3 points, 8.5 rebounds, 1.8 assists, 1.0 steals and 1.3 blocks in 30.5 minutes per game. He was again named to the Pac-12 All-Academic Honorable Mention team.
As a redshirted senior in 2013–14, Brandt finished 11th in the Pac-12 in field goal percentage with 51.1 percent (138-for-265), and earned second-team Pac-12 All-Academic honors. On 18 December 2013, he recorded a career-high 27 points against Towson. In 30 games (all starts), he averaged 12.6 points, 3.9 rebounds and 1.5 assists in 25.4 minutes per game.
On 16 June 2014, Brandt signed a three-year deal with the Sydney Kings of the National Basketball League. The following month, he joined the Penrith Panthers of the Waratah League in preparation for the 2014–15 NBL season. With the Panthers, he played alongside his brother, Louis. In six games for the Panthers, he averaged 25.3 points and 10.2 rebounds per game.
On 13 January 2015, Brandt was ruled out for four to six weeks with a knee injury he sustained playing for the Kings on 31 December 2014 against the Townsville Crocodiles. He returned to action on February 6 and played out the season, going on to earn the 2014–15 Rookie of the Year award after averaging 7.4 points and four rebounds per game while shooting at nearly 50 percent from the field over 21 games.
Brandt entered the 2015–16 season with a reduced role thanks to the Kings' off-season acquisition of Julian Khazzouh. Brandt consequently averaged just 3.4 points in 10.8 minutes per game over the first 11 games of the season, but over the final eight games to close out 2015, Brandt averaged 10.5 points in 21.6 minutes per game. With a late December injury ruling Khazzouh out for the rest of the season, Brandt was forced to take on a much bigger role heading into 2016. He went on to play in all 28 games for the last-placed Kings in 2015–16, averaging 8.1 points, 5.3 rebounds and 1.2 blocks in 19.1 minutes per game.
On 23 February 2016, Brandt signed with Neptūnas Klaipėda of Lithuania for the rest of the 2015–16 LKL season. He helped Neptūnas reach the Finals where they were defeated 4–1 in the best-of-seven series by Žalgiris. In 21 games for the club, he averaged 4.6 points and 3.8 rebounds per game.
On 12 May 2016, Brandt signed a two-year deal with the Perth Wildcats. Brandt played a sparing role for the Wildcats over the first 21 games of the season, recording just one double-digit scoring game in that time. He came into the team's game against the Cairns Taipans on 20 January 2017 averaging 4.9 points and 2.4 rebounds in 11 minutes per game. In the game against Cairns on 20 January, Brandt played a season-high 30 minutes off the bench and had season-best figures of 17 points and 11 rebounds in an 84–78 overtime win. Brandt had an impressive back-end of the year for the Wildcats as he scored in double figures in four out of the final 13 games of the season, and provided a spark off the bench at the centre position. The Wildcats finished the regular season in third place on the ladder with a 15–13 record, after having started the season with a 7–9 record that saw them sitting in last place in mid-December. They went on to sweep the second-seeded Taipans in the semi-finals to make it through to the best-of-five NBL Grand Final series. After scoring nine points in a Game 1 win over the Illawarra Hawks in Perth, Brandt stepped up to cover the loss of Matthew Knight in Game 2 in Wollongong. He recorded 15 points and 11 rebounds in a Game 2 win that saw the Wildcats take a 2–0 lead in the series. The Wildcats returned home for Game 3 and took out the championship with a 3–0 series sweep of the Hawks; Brandt had six points, seven rebounds and four assists in 20 minutes off the bench in Game 3. He appeared in all 33 games for the Wildcats in 2016–17, averaging 6.0 points, 2.9 rebounds and 1.1 assists per game.
On 17 July 2017, Brandt signed a two-year contract extension with the Wildcats, thus keeping him in Perth until the end of the 2019–20 season.
In 2011, Brandt was part of the Australian University national team that played at the 26th World University Games in Shenzhen, China. In 2014, he was part of the Boomers team that played in the four-game Sino-Australia Challenge series.
In June 2017, Brandt was named in a 20-man Boomers squad ahead of the 2017 FIBA Asia Cup. A month later, he was named in the final 12-man squad.
Brandt is the son of John and Lorraine Brandt, and has two brothers, Seamus and Louis.