Burgess began his career at Arsenal's academy and after he was released he went on to play with the youth and reserves teams at non-League Bishop's Stortford before deciding to study history at the University of Birmingham. Whilst in his second year university, Burgess earned a trial at Middlesbrough through a coach of the University's first team.
Middlesbrough
He impressed at Boro and he signed a two-year contract in July 2012. He made his professional debut on 4 May 2013 in a 2–0 defeat away at Sheffield Wednesday.
He joined Hartlepool United on loan in August 2013. The loan deal was extended until the end of the season in December. Burgess scored his first goal in professional football in a 5–0 win for Hartlepool in a Football League Trophy game against Bradford Cityin September 2013.
Peterborough United
On 19 August 2014, Burgess signed on a month's loan for Peterborough United. He completed a single game on loan, a 2–1 home defeat by Sheffield United, before completing a permanent transfer on 21 August 2014. Burgess signed a four-year contract for an undisclosed fee.
On 25 June 2015, Burgess signed for south coast club Portsmouth as part of the summer overhaul at the club by new manager Paul Cook. He went on to make his debut on 11 July 2015, in a pre-season friendly against local Conference South club Havant & Waterlooville. During the 2015-16 season, in which Portsmouth reached the play-off semi-finals, Burgess made 43 appearances in all competitions, partnered in most games by either Matthew Clarke or Adam Webster.
2016–17 season
Following a successful first campaign for Pompey, during which he established himself as the club's first-choice centre back, Burgess began the 2016-17 season as one of the team's central figures. In total, Burgess made 45 appearances and scored four goals over the course of the season, as Portsmouth won the League Two title. Burgess, along with teammate and fellow defender Enda Stevens, was named in the League Two team of the year; a reward for their part in Portsmouth's league-best defensive record.
Union SG
Burgess turned down a contract extension at Portsmouth and on 7 July 2020 joined Belgian First Division B club Union SG, signing a three-year deal with the option of an additional year.
Personal life
He earned a BA Hons in History part-time at Teesside University having previously studied History at University of Birmingham before his move to Middlesbrough.
