Wenger's visit had been planned for some time, and was originally teased by the club's manager Lucien Favre during Ramsey's unveiling.
The 72-year-old was pictured placing a friendly hand on Ramsey's back as the pair shared a joke in training.
Wenger knows the 31-year-old midfielder well, as he signed him from Cardiff after the club's impressive FA Cup run in 2008 and, managed Ramsey for all but one of his 11 seasons at the Emirates.
He said of the midfielder: "He had a few injuries in Italy. He needs time to get back to his best, physically. He's creative, a finisher."
On starting a new chapter of his career with Nice, Ramsey said: "I am very happy to be here and to be part of the project. I am very excited to arrive in this young and talented team.
"I feel very good. I trained well this week and discovered a staff fantastic. My experience at Juventus took me out of my comfort zone.
"I had been at Arsenal for a long time. Today I have a new opportunity and I can't wait to start this adventure."