The deal marks a return to the A-League for 23-year-old Burgess, who played one match for Sydney FC in 2014 and represented the Newcastle Jets five times a year later.
His form with NSW champions Sydney Olympic FC, in which he scored seven goals in 23 appearances, impressed Phoenix coach Mark Rudan.
The deal was sealed when Burgess impressed in a pre-season match against the Phoenix
''He has tasted A-League experience before but I feel that he has plenty more to show," Rudan said.
''We have the perfect environment for him to develop and show that true potential he holds."
Burgess began his career at Rockdale City Suns shortly after Rudan left as head coach in 2013.
The Phoenix recently missed out after entering contract discussions with two big-name African internationals - Nigerian striker Obafemi Martins and Ghanaian midfielder Michael Essien.
They open their campaign next week at home to Newcastle.
