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. While attending Westlake, he played basketball for the North Harbour juniors; from 2010 to 2012, he played for the North Harbour U17s, U19s and U21s. In 2012, Webster played for the Auckland Pirates, where in two games, he recorded a total of two points and two assists. The Pirates went on to win the 2012 championship with an 89–83 win over the Wellington Saints in the grand final. In August 2012, Webster joined the New Zealand Breakers as a non-contracted development player for the 2012–13 NBL season. In December 2012, he signed a National Letter of Intent to play college basketball at the University of Nebraska–Lincoln. In April 2013, Webster signed with the Waikato Pistons for the 2013 New Zealand NBL season. In 15 games for Waikato, he averaged 18.5 points, 3.9 rebounds, 4.4 assists and 2.0 steals per game. He had never heard of Nebraska when he was recruited, but signed with the team anyway.
College career
Freshman year
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 while helping the Huskers reach the NCAA Tournament for the first time since 1998. He led Nebraska with 63 assists and was also among the team leaders in steals. Webster reached double figures four times, including a season-high 14 points against Georgia, and paced the squad in assists eight times. His season-best was five assists on three occasions.
Sophomore year
As a sophomore in 2014–15, Webster emerged as one of the first Huskers off the bench, backing-up starting guards Terran Petteway and Shavon Shields. He fell out of the rotation early in Big Ten play but found a role as the Huskers' energy guy off the bench and his improved defense showed in other facets of his game. In 30 games, he averaged 3.9 points, 1.9 rebounds and 1.2 assists in 18.4 minutes per game. Webster called the season "hugely disappointing" since his work in practice did not translate to higher production than as a freshman.
Junior year
As a junior in 2015-16, Webster joined the Nebraska starting lineup. He averaged 10.1 points, 4.1 rebounds and 1.9 assists in 27.7 minutes per game.
Senior year
As a senior in 2016-17, Webster averaged 17.0 points, 5.1 rebounds and 4.0 assists in 34.7 minutes per game. Leading up to the NBA draft, many thought Webster could be a "second-round sleeper."
College statistics
Professional career
Webster went undrafted in the 2017 NBA Draft. He joined the Golden State Warriors for the 2017 Las Vegas NBA Summer League. He signed with Skyliners Frankfurt in Germany for the 2017-2018 season. He posted 14.9 points, 3.6 rebounds, and 3.8 assists per game in his rookie season. Webster signed with the Turkish team Galatasaray on 7 August 2018. On 7 August 2019, Webster renewed his contract with the Turkish club for two more seasons. On 15 July 2020, Webster returned to the NBL and New Zealand and signed a one-year contract with the New Zealand Breakers.
Webster is the son of Tony and Cherry Webster. Tony was a standout athlete in his own right, earning first team All-WAC honors at Hawaii in 1983 and ranking fourth on Hawaii’s career steals list before playing professionally in New Zealand. His older brother, Corey, was playing professionally for Ironi Nahariya of the Israeli Basketball Premier League.
