Burgess's grandfather is retired Scottish international footballer Campbell Forsyth. His father, Stuart Burgess, was also a professional football player.
Burgess joined the Fulham Academy in 2011 from ECU Joondalup and signed a professional contract with the club in July 2013. He made his first team debut for Fulham, in a 2–1 away loss in the opening match of the 2014–15 Championship season on 9 August 2014 against Ipswich Town at Portman Road.
On 15 January 2015, Burgess signed a contract extension with Fulham until June 2017, with an option for another year, and on the same day signed on loan for Scottish Premiership club Ross County until the end of the 2014–15 season.
Burgess joined Cheltenham Town of the National League on loan for the remainder of the 2015–16 season on 26 January 2016.
On 18 July 2016, Burgess joined League One club Oldham Athletic on a six-month loan deal. He made his debut on 6 August 2016 in a 3–0 loss to Millwall. He scored his first goal for Oldham in a 1–1 draw with Oxford United on 10 December 2016.
On 6 January 2017, he moved to Bury on loan for six months.
On 6 June 2017, Burgess joined Scunthorpe United on a three-year contract.
Burgess played for Scotland U-19 team and took part in the 2014 UEFA European Under-19 Championship qualification campaign, playing the full game against Latvia in a 1–1 draw.
In September 2014 Burgess switched his allegiance permanently to Australia. He was named in the Australia squad for the 2014 AFC U-19 Championship held in Myanmar.
16 March 2015, Burgess was selected as one of twelve overseas based players in a squad of twenty three by head-coach, Aurelio Vidmar, to take part in the Australian Olyroos' qualification campaign on the road to Brazil 2016 Olympic Games. The first stage of qualification began in a tournament held in Kaohsiung City, Taiwan, against minnows Hong Kong, Myanmar and hosts Taiwan. The Olyroos progressed past this qualification tournmanet to qualify for the AFC U-23 Championship, which doubles as the final qualification round for the AFC for the Olympics. On 23 December 2015, Burgess was again selected by Vidmar to form part of the Olyroos squad for the 2016 AFC U-23 Championship held in Doha, Qatar between 14–30 January 2016.As of 4 July 2017
National League: 2015–16