Burgess is rated one of the best fitness coaches in the game and enjoyed his spell working the Merseyside club.
After making a return to Port Adelaide, the Australian is now close to agreeing personal terms with the north London club and jumped at the chance to make a return to the Premier League.
Burgess is set to take charge of medical, fitness, psychology and performance analysis at the Gunners and will report back to Arsene Wenger.
Burgess, speaking in The Sun, said: “Reaching this decision has been one of the toughest decisions in my professional career.
“When the opportunity came up to return to Port Adelaide I had no hesitation in returning.
“Port Adelaide is like family and once you’ve worked in this environment with so many outstanding people it is very difficult to leave.
“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.”
“I look forward to continue having a relationship with Port Adelaide from afar and thank the entire club for their support and many great memories over two stints.”
The 43-year-old worked at Liverpool between 2010 and 2012 where he worked under three different managers and was also responsible for managing the Australia players fitness at the 2010 World Cup in South Africa.
* ARSENAL have brought in Huss Fahmy from Team Sky to take care of contracts, writes Darren Lewis.
Current negotiator Dick Law is set to remain with Fahmy in a supporting role.
Fahmy’s arrival, however, will address the issue of the Gunners being vilified for allowing important players to run down their contracts.
Alexis Sanchez, Mesut Ozil and Alex Oxlade-Chamberlain are all going into the final year of their deals.