Fiorentina finished a disappointing 16th in Serie A last season and Montella will be hoping Ribery's talent can help turn their fortunes around.
"He is an extraordinary player, he's eager and we believe he can express himself here," Montella told Sky Sport Italia .
"He had his first training session today, but I was the only other one there, so I put my boots on after many years and had a kick-about."
Fiorentina open their Serie A season at home to Carlo Ancelotti's Scudetto hopefuls Napoli on Saturday.
Having just touched down in Italy, Montella hinted that it's unlikely Ribery, now 36, will feature quickly.
"We'll see over the next few days how he responds to training and he is very determined," he said.
"But we should take it easy. He was a little rusty, as was I."
Fiorentina consultant Joe Barone, who works alongside new president and owner Rocco Commisso, claimed Ribery's decision to join Fiorentina was an easy one despite getting more lucrative offers from elsewhere.
"Choosing Florence is easy! It's the city of art, of love, he already speaks Italian pretty well and his wife loves Florence," Barone said.
"He was offered a lot of money elsewhere, but he chose Fiorentina for a club that is growing and he saw at the airport how important the fans are in that choice.
"He is training, is very eager and today is a very important moment for Fiorentina.
"It's exciting fans throughout Tuscany and the world, I saw so many people at the airport and hope there will be many more at the stadium tomorrow to celebrate Ribery."