Furuhashi became the latest Japan international to join the club when he arrived in Glasgow from Vissel Kobe in July.
The 26-year-old follows in the footsteps of Nakamura, who scored 33 goals in four seasons with Celtic from 2005, including a memorable winner against Manchester United in the Champions League.
Speaking through an interpreter, Furuhashi said of Nakamura: “I remember him playing for Celtic and the supporters must remember him very well. I remember the free-kick he scored against Manchester United.
“I’m looking forward very much to playing here in front of the supporters and also to share the excitement together.
“Celtic have a great history and a wonderful team. I feel very happy and honoured to be here.”
Furuhashi made his Celtic debut as a substitute in Saturday’s Scottish Premiership defeat against Hearts on the opening weekend of the season.
That made it three games without victory in all competitions for new Celtic manager Ange Postecoglou, who has already seen his side crash out of the Champions League.
Furuhashi insists Celtic will get back on track as they try to dethrone champions Rangers.
“At the moment I am thinking about the current situation and concentrating on what I can do,” he said.
“It was very exciting and fun to make my debut. I have to concentrate on what I am doing and I hope to contribute to the team as much as I can.
“Celtic have great players and the manager is wonderful. If we can focus, the results will follow.”