The 26-year-old will join from Vissel Kobe subject to the satisfaction of usual conditions and international clearance.
Furuhashi, who has six caps and three goals for Japan, is the J1 League’s top scorer with 14 goals in 20 games.
“I think he will add something special to our squad and I am sure the way he plays will excite our supporters. We look forward to welcoming him to Celtic."
Furuhashi can operate in wide areas or as a central striker and becomes the latest recruit following the addition of Israeli forward Liel Abada.
He has scored six goals in his last four games for Vissel Kobe, including a hat-trick against new boss Postecoglou’s former club Yokohama F Marinos.
A team-mate of Andres Iniesta and Thomas Vermaelen, his goals have amounted to 11 points, helping the club up to a third place after 20 games.
No player has attempted more shots (78) in the Japanese top-flight, while he is in the top ten for dribbles (83).
Furuhashi thrives on through balls with nine of his 14 goals coming from latching on to passes behind the opposition defence, while he is a creative finisher.
Celtic have had success in the Japanese market before with Shunsuke Nakamura who is still playing in the top-flight at the age of 43.