He played four college seasons for the Nebraska Cornhuskers, earning second-team All-Big Ten as a senior in 2017.

Born in Auckland, Webster attended Westlake Boys High School where he led them to the National Secondary Schools Basketball Championships in October 2012, scoring 24 points en route to garnering tournament MVP honours.

[citation needed] Webster made his debut in the New Zealand National Basketball League (NZNBL) in 2012 with the championship-winning Auckland Pirates.

[1][2][3] In August 2012, Webster joined the New Zealand Breakers as a non-contracted development player for the 2012–13 NBL season.

[4] In December 2012, he signed a National Letter of Intent to play college basketball at the University of Nebraska–Lincoln.

[1] As a freshman for the Nebraska Cornhuskers in 2013–14, Webster was an immediate contributor, averaging 3.9 points, 2.1 rebounds and 2.0 assists in 32 games (30 starts) while helping the Huskers reach the NCAA Tournament for the first time since 1998.

[8] Webster called the season "hugely disappointing" since his work in practice did not translate to higher production than as a freshman.

[13] On 15 July 2020, Webster signed a one-year contract with the New Zealand Breakers, returning to the team for a second stint.

[25] Webster returned to the Wildcats for the 2023–24 NBL season[26] and averaged 8.9 points, 2.8 rebounds, 2.7 assists and 0.9 steals per game, while shooting at 46 per cent from the field.

[33][34] In 2012, Webster represented New Zealand at the FIBA World Olympic Qualifying Tournament, where he averaged 13.5 points per game.