Arsene Wenger is believed to be a big fan and is said to have "hand-picked" Burgess for the role.
The club's existing fitness coach, Tony Colbert, is likely to be asked to report into Burgess, who is also expected to work closely with Shad Forsythe, appointed as Arsenal's head of athletic performance enhancement after his work with Germany at the 2014 World Cup.
The fitness guru is under contract with Port Adelaide until the end of this season, but will be allowed to leave to join Arsenal in the next few weeks if the South Australian club are satisfied with financial payment offered by the Gunners, according to The Advertiser.
While Arsenal may not be extremely active adding new players, the club have been active adding new backroom staff and other personnel, perhaps indicating the club's commitment to making the necessary changes as we head towards the later stage of Arsène Wenger's time at Arsenal.
"Reaching this decision has been one of the toughest decisions in my professional career", he said.
It's happening! Wenger goes Aussie to shake-up Arsenal fitness team
Reports last week claimed that Burgess, who worked at Liverpool between 2010 and 2013 under Kenny Dalglish, Roy Hodgson and Brendan Rodgers, was set to move to Arsenal to take charge of their medical, fitness, psychology and performance analysis.
However, the opportunity to return to the English Premier League and work at one of the world's most successful sporting organisations in Arsenal is an opportunity I simply couldn't refuse. Burgess thanked Port for their unending support and revealed his excitement at returning to England.
Burgess will start his new role at Arsenal in July but will return to Adelaide later that month.
"But what we've been able to do is work with Arsenal to enact a transition process which limits any impact or disruption to our football program for this year, and retain Darren's expertise for our 2018 planning".