Both players were allowed to leave the Gunners this summer, with Wilshere joining the Hammers on a free transfer and Perez following his Arsenal teammate for a reported fee of £4m.
Despite having never played together, the England international insists that he has seen enough from the 29-year-old forward during training sessions to know that he will impress at their new club.
"To be honest, I've never played a game with him but I trained with him because last season we were both in a similar situation as we'd both been told we could leave," the midfielder told the club's official website.
"He decided to go to Deportivo and I decided to stay and fight for my place, but there was a period of three or four weeks when we were in a group who trained on our own and he has got real quality.
"He's calm in front of goal, he can finish, he's got a personality on the pitch, he's got character and I'm looking forward to finally getting to play alongside him, you know."
Wilshere and Perez will have a chance to play together when West Ham host Bournemouth in the Premier League on Saturday.