Burgess, who has been the high performance manager at AFL club Port Adelaide since 2012, is close to agreeing a deal with Arsenal with a announcement expected in the coming days, UK media reports.
Burgess is reported to begin his new role at Arsenal within the next fortnight.
The move has been driven through by Arsenal's chief executive Ivan Gazidis – who promised fans earlier this year that changes would be made – and has been rubber-stamped by manager Arsene Wenger.
The highly-rated Burgess will report directly to Wenger but is expected to be given a wide-ranging brief to include overall control of medical, fitness, psychology and performance analysis at the club, as well as working with the academy.
Burgess is known as the highest-paid fitness coach in the AFL and has been the target of European and American sporting franchises for many years. His offer from Arsenal is reportedly a seven-figure sum.
Burgess' contract with Port Adelaide ends at the conclusion of the AFL season in October, with the AFL club said to be seeking compensation from Arsenal for poaching him.
This will be Burgess' second stint in the Premier League having worked with Liverpool between 2010-2012 after spending three years as the head of fitness for Football Federation Australia and helping the Socceroos in their 2010 World Cup campaign.
At Liverpool, Burgess held the title of head of fitness and conditioning under three different managers, Kenny Dalglish, Roy Hodgson and Brendan Rodgers.
