Burns, 27, is on his way to Japan to undergo a medical after second-placed FC Tokyo triggered a release clause in his Phoenix contract with an offer of around $300,000.
The Japanese sports website Sponichi Annex reported that the AFC 2015 Asian Cup winner, who notched 13 goals last season for Ernie Merrick's men as they forced their way into the play-off places, has agreed terms to replace Japan international Yoshinori Muto, who signed a four-year deal with Bundesliga side Mainz in May.
Tokyo, whose coach Massimo Ficcadenti is the first Italian to lead a J.League club, has been tracking Burns since late May.
Phoenix general manager David Dome confirmed the Wellington club had accepted the offer, and added: “We expected this to happen given the season Nathan had with us.
“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.”
The Japan trail appeared to have gone cold before heating up again late last week when a formal offer was tabled to Phoenix, where Burns has a year remaining of his two-season contract.
He also had options elsewhere in Asia and also Europe and will have a hard act to follow in Tokyo with Muto bagging 10 goals in 17 games this season.
Burns, who led Australia’s attack alongside Tim Cahill in last month’s 2-1 FIFA World Cup qualifying win over Kyrgyzstan in Bishkek, is understood to have been offered a two-year contract by the club which lies six points adrift of leader Urawa Reds at the half-way mark of the competition.
The move will be a second coming to Asia for Burns, whose injury blighted two-year spell at K-League Incheon United yielded just three appearances.
The Adelaide United product's first foray overseas took him to Greek giant AEK Athens, where he was on the books for four years before moving to Incheon.
His highly impressive A-League stint precipitated his re-emergence with the national team, for whom he now has 12 caps.
Burns also had a brief loan spell at the Newcastle Jets prior to signing for Phoenix a year ago.
He will join fellow countryman Mitchell Duke, of rock bottom Shimuzu S-Pulse, in Japan’s top flight.