The Gunners announced on Monday that the Ivory Coast international was to join the club, subject to a regulatory process, from the current Ligue 1 champions.
Gervinho netted 28 goals in 67 appearances for the Stade Lille-Metropole outfit, scoring 15 times last season as Lille captured their first league crown since 1953/54.
And Van Persie, current touring Asia with the Arsenal squad, told the club's official website that he is looking forward to seeing the Gunners' new recruit in action, having followed his progress in France last term.
However, he urged fans not to expect miracles from him straight away, insisting that any new player needs time to adjust to fresh surroundings and different team-mates.
"I know him from the highlights of the French league," he said. "I’ve seen him play a couple of times for the Ivory Coast and I’ve been speaking to [Emmanuel] Eboue and he was very positive about him.
"The things I’ve seen look great but we will have to wait and see how he adapts. Every new player that comes in needs time so he will need a couple of months to feel at home and hopefully he can play his best football."
The Dutchman also welcomed the competition for places that Gervinho's arrival will bring to the Emirates Stadium outfit.
"I think it is a good thing that you have competition. Everyone needs competition because no one really wants to go to sleep," he said.
"I think in the ideal world, no one is really sure of his place. Maybe the captain and the goalkeeper but all the others shouldn’t be known before that they will play. It’s good to have competition and be on your toes."
And Van Persie encouraged manager Arsene Wenger to continue adding to the squad, as the Gunners seek to end a six-year silverware drought.
"The way I feel now is that new signings are more than welcome, why not? Every other team is buying quality players so hopefully we will do the same. If you look at Manchester City buying loads of good players and Liverpool is doing it now and Manchester United has been doing it for years. If everyone is doing something you need to do it as well."
