In March 2012, it was announced that Rhys Browne, a strong, pacey centre-forward from Romford, would be joining the Canaries as an Academy Scholar in the summer of 2012. He had previously played with Interwood before joining Norwich at the age of 15.

He was part of the squad which won the FA Youth Cup and Norfolk Senior Cup in 2013. Rhys made 16 appearances for the Under-18s during 2012/13

Rhys was released at the end of the 2013/14 season. He joined Charlton and remained with them until May 2015. During this period, he was loaned to VCD Athletic of the Isthmian League.

In June 2015, he made his international debut for Antigua and Barbuda as a substitute against St Lucia. His first international start came in the return leg which Antigua won 4-1. He scored his first and only international goal on March 21 2018 in a 3-2 friendly win over Bermuda. To date, he has 10 international caps.

After a successful trial, he signed for Aldershot at the beginning of August 2015.

On 21st June 2016 Browne signed for Grimsby Town for an undisclosed fee after scoring six goals in 37 National League games in 2015/16.

Browne was loaned in January 2017 to Macclesfield Town until the end of the 2016/17 season. He helped them reach the final of the FA Trophy, scoring at Wembley in the defeat to York City. In total he played 24 games for Macclesfield, scoring six goals.

On 16th June 2017, Rhys signed a two year contract with Yeovil for an undisclosed fee. Browne's father Steve also played at Huish Park for Yeovil in the 1990s.

Browne and Yeovil were relegated to the National League on 27th April 2019 following a 2-2 draw with Northampton. Browne was one of nine players released by Yeovil at the end of the 2018/19 season. He had made 72 appearances for Yeovil, scoring seven goals.

In July 2019, he joined Port Vale on trial, playing for them against Kidsgrove on 6th July 2019 and Fleetwood on 17th July 2019. Browne signed for Vale on 27th July 2019. Given the number 17 shirt, he made his debut for the Valiants on 14th September 2019 in a 1-0 win over Plymouth.  

On 29th August 2020, Browne left Port Vale having had his contract terminated at his request. Manager John  Askey cited family reasons for the player's departure, adding that "it was a shame because he was doing well"

Browne signed for National League side Wealdstone on 22nd December 2020. He switched to fellow National League side Sutton United on 6th January 2021. He played 14 games for Sutton as they won the National League title. He then returned to Wealdstone on 22nd June 2021 signing a one year contract.

Despite scoring seven goals in 12 appearances at the start of the 2022/23 season for Wealdstone, he was allowed to join their rival Woking on 15th October 2022 on a two year deal, with an option of a third year. He moved on to Barnet on 14th May 2024.