His father, Mark Burgess who died of Motor neurone disease, was also a rugby league footballer who played for Nottingham City, Rochdale Hornets, Dewsbury Rams and Hunslet;[6] while his mother Julie is a teacher, currently employed at The Scots College in Bellevue Hill, Sydney.

[8] Burgess attended Castle Hall Academy to receive a secondary education before becoming a professional rugby league footballer.

Burgess first featured in three of the four pre-season friendlies of the 2011 season, playing against Halifax, the Dewsbury Rams and the Wakefield Trinity Wildcats.

He made his Super League début in Round 8 against the London Broncos off the interchange bench in the Bradford Bulls' 24-22 win.

On 6 August, it was announced that Burgess had signed a one-year deal with the South Sydney Rabbitohs for 2013, joining brothers Sam, Luke and George.

In Round 15, Burgess made his NRL début for South Sydney against the Parramatta Eels, playing off the interchange bench in the 30-10 win at ANZ Stadium.

[16] In Round 21 against the Newcastle Knights at Barlow Park in Cairns, Burgess scored his first NRL try in South Sydney's smashing 50-10 win.

[24] In December, Burgess trialled and trained with NFL teams the Seattle Seahawks and Buffalo Bills after he attracted interest from the clubs.

Burgess made 27 appearances for Souths in total as the club finished 3rd on the table at the end of the regular season and reached the preliminary final before being defeated by eventual premiers the Sydney Roosters 12-4.

[39] Burgess began the 2019 NRL season in good form as the club won 10 of their first 11 games to sit on top of the table.

Following South Sydney's Round 13 loss against Newcastle Knights, Burgess was ruled out of action for 4–6 weeks with an ankle injury.

[40][41] Burgess made a total of 19 appearances for South Sydney in the 2019 NRL season as the club finished 3rd on the table and qualified for the finals.

However, for the third straight year Souths would fall short of a grand final appearance losing to Penrith 20-16 at ANZ Stadium.

[48] In round 6 of the 2021 NRL season, he scored the winning try for South Sydney in their 18-14 golden point extra-time victory over the Wests Tigers.

[55] In the third group stage match at the 2021 Rugby League World Cup, Burgess scored two tries for England in a 94-4 victory over Greece.

[60] On 7 February, it was announced that Burgess had signed a three-year deal with English side Huddersfield which is due to start in the 2025 Super League season.