Vissel Kobe said on their website the deal was subject to a medical. It did not reveal the transfer fee or other details.
Furuhashi will join a Celtic side led by former Yokohama F. Marinos head coach Ange Postecoglou, who moved to Scotland last month having led the Marinos to the J1 League title in 2019.
Furuhashi, 26, made his debut for Japan against Venezuela in November 2019 but had to wait more than a year for his second cap, which came in a 3-0 win over Korea Republic in March.
He has played six times for the Samurai Blue, scoring twice in a 14-0 thrashing of Mongolia in World Cup qualifying in March before netting against Tajikistan last month.
Furuhashi was part of the Vissel Kobe side that won the Emperor's Cup in 2019 and featured in the AFC Champions League as the club made their debut in the continental club championship last year.