Phoenix general manager David Dome admitted his club had accepted it would lose Burns following 27-year old's sensational season when he netted 13 goals in 24 matches for the Kiwi club.
"We expected this to happen given the season Nathan had with us," Dome said.
"It became even more likely when he won the Johnny Warren medal for the best player in the A-League.
"Ernie Merrick has been looking at alternatives for some time and will continue to do so.
"Nathan has been terrific for the Phoenix and we wish him well for the future."