Vermaelen, who joined the Gunners from Ajax this summer, scored two goals in the win over Wigan on Saturday.
Van Persie had a spat with Vermaelen during the pre-season Ajax Tournament two years ago.
Van Persie said: “He is hard and played very strong on me physically and I was a little bit upset about that. So I told him in nice words!
“Now I’m happy he is on my side. In training everyone mixes up so I play against him. He is tough and it’s good because I am training against proper defenders.”
He added: “He is raised in Holland. I am not saying every Dutch player is good technically but when you are raised in Holland – especially at Ajax, Feyenoord or PSV – you are brought up getting the ball, moving it first touch, move again, pass, move.
“He was at Ajax since 15 so it is in his system for a long, long time.”