Giroud, who is part of Laurent Blanc's Euro 2012 squad, is thought to command a transfer fee in the region of £13million. The 25-year-old scored 25 goals for his club last season to help Montpellier win the Ligue 1 title, igniting the interest of several top clubs.
However, it appears Arsenal are set to add the promising Frenchman to their squad, and Wenger told French TV station TF1: "Giroud didn't play much (at the Euros so far), but he's going to be an Arsenal player 90 per cent next season."
Wenger added: "I think he has exceptional potential and will integrate very well in our collective and our way of playing. He is a real team player and knows how to combine with other players and I'm sure he will do well with us."
Wenger is working at the European Championship as a media pundit, and has been impressed by the displays of Germany's Lukas Podolski, who has already joined the ranks at the Emirates for next season.
"Podolski did a great job for the German team, he has superb team work," the Arsenal boss said.
"He plays in a cautious way sometimes, but he's still scored a very important goal against Denmark for his 100th cap.
"I am very happy with what I've seen from him."
Once the deal for Giroud is complete, Arsenal could then look to offload some of their fringe players, including Denmark striker Nicklas Bendtner and Morocco international Marouane Chamakh as well as Mexico forward Carlos Vela and Brazilian midfielder Denilson.