In 2011, Browne enrolled at West Virginia University and joined the Mountaineers basketball team. He played with the team for four seasons, averaging 6.2 points per game. As a senior, he averaged 7.0 points per game. He sprained his ankle in February 2015. After graduating, Browne made himself eligible for the 2015 NBA Draft, but went undrafted.
Professional career
Puerto Rico (2015–2019)
In 2015, Browne joined the Maratonistas de Coamo of the BSN league in Puerto Rico. He played in a total of 7 games, averaging 4 points and 1.9 assists per game. However, he did not play in the 2016 season. That year, the Atléticos de San Germán acquired the rights to Browne. He said in an interview that he took the off-year to prepare himself physically for the 2017 season. Browne began the 2017 season as San Germán's starting point guard. He led the league in assists all through the season, finishing with an average of 7.5 per game. Browne's performance led his team into the playoffs, where they were eliminated by the Piratas de Quebradillas. Browne finished the season with averages of 11.9 points and 6.4 rebounds per game, and improved to 14.6 points, 8.2 rebounds, and 7.8 assists per game in the playoffs. In July 19, he was named the league's Most Improved Player. Two weeks later, he was awarded the Most Valuable Player. On June 7, 2018, Browne re-signed with Atléticos de San Germán for the 2018 BSN Season. In 19 games played during the 2018 season, he averaged 17.1 points, 6.3 rebounds, 7.2 assists and 1.5 steals per game. On June 11, 2019, Browne re-signed with Atléticos de San Germán for the 2019 BSN Season.
Israel (2017–2019)
On August 2, 2017, Browne signed with the Israeli team Ironi Nes Ziona for the 2017–18 season. On April 28, 2018, Browne recorded a career-high 32 points, shooting 6-of-10 from three-point range, along with six rebounds and six assists in a 101–91 win over Maccabi Rishon LeZion. Browne helped Nes Ziona to reach the 2018 Israeli League Playoffs, where they eventually lost to Maccabi Tel Aviv in the Quarterfinals. On July 1, 2018, Browne signed a one-year contract extension with Ironi Nes Ziona. On January 19, 2019, Browne recorded a season-high 28 points, shooting 9-of-11 from the field, along with four rebounds, six assists and two steals, leading Nes Ziona to a 103–93 comeback win over Ironi Nahariya. He was subsequently named Israeli League Round 15 MVP. In 36 Israeli League games played during the 2018-19 season, he averaged 13.9 points, 4.8 rebounds, 4.9 assists and 1.1 steals per game, while shooting 39.5 percent from three-point range. Browne helped Nes Ziona reach the 2019 Israeli League Playoffs, where they eventually were eliminated by Hapoel Eilat in the Quarterfinals.
Turkey (2019–2020)
On September 23, 2019, Browne signed with Darüşşafaka Tekfen of the Turkish Basketbol Süper Ligi as an injury cover for Joe Ragland. He averaged 10.8 points and 3.6 assists per game. On July 5, 2020, Browne parted ways with the team.
Italy (2020–present)
On July 14, 2020, Browne signed with Dolomiti Energia Trento of the Italian Lega Basket Serie A.