West Ham United Browne joined
West Ham United at the age of eight and progressed through the academy at the club prior to signing his first professional contract on 12 November 2015. On 18 August 2016, Browne made his senior debut in a
Europa League fixture against
Astra Giurgiu. The game finished 1–1 and Browne replaced
Gökhan Töre in the 75th minute. After making a tackle in the middle of the pitch, Browne ran for around before passing to teammate
Michail Antonio before the right winger missed a clear chance to score.
Wigan Athletic (loan) On 20 January 2017, Browne joined struggling
Championship club
Wigan Athletic on loan until the end of the
season. He made his debut and only appearance on 29 January, where he came on as a second-half substitute in their 4–0
FA Cup defeat to
Premier League giants
Manchester United. Wigan went on to suffer relegation to
League One at the end of the divisional campaign.
Oxford United (first loan) On 24 July 2018, Browne joined established League One club
Oxford United on a season-long loan. He made his league debut, coming on as a substitute, during a 2–0 home defeat to
Fleetwood Town, their second game of the season. Browne scored his first goal for Oxford in a convincing 2–0 win against
Coventry City on 14 August, in the first round of their
EFL Cup campaign. His first league goal, which was referred to as a "superb solo goal", came in a 3–2 home defeat to
Accrington Stanley a week later.
Middlesbrough On 26 July 2019, Browne signed a four-year deal with
Championship club
Middlesbrough for an officially undisclosed transfer fee.
Oxford United (second loan) Browne re-joined
Oxford United on 9 January 2020 on a loan deal until the end of the 2019–20 season.
Oxford United In January 2022 Browne signed a two-and-a-half-year contract with
Oxford United for an undisclosed fee. Browne's contract included the option of an extra 12 months.
AFC Wimbledon On 14 January 2025, Browne signed for
League Two side
Wimbledon on a deal until the end of the 2024/25 season. The signing was financed by
John Green through
EA Sports FC streaming funds. On 27 June 2025, the club announced he had signed a new two-year deal. ==Style of play==