The club's record signing has endured an up and down debut season at the Emirates.
But after scoring in Sunday's 2-1 FA Cup semi-final win over Sheffield United, Arteta is confident Pepe has finally settled at the club.
"I'm very excited about what he can bring [in the future] and what he's bringing to the team this season," said Arteta. "I think he's made a click and I think he realises what he needs to do for the team when we don't have the ball.
"I'm so pleased today, you've seen his defensive actions were incredible with what he's doing, and then with the ball he gives us that creativity and flair that we need and big teams need. He's always unpredictable with what can happen when he's got the ball at his feet, so I think he's [heading] in the right direction.
"I really liked him from the past. I didn't know him personally, but I think he is a player with incredible potential, but he needs to be decisive in every game and he needs to take care of moments in the game when he disconnects himself a little bit. He cannot do that, and I will be very persistent with him to try to change that because at his best, he can make the difference for the team."
On Pepe's struggles to adapt in North London, Arteta added: "It's very important to try and understand a player and find out what his feelings are, how hard it's been to adapt to a new country and a language that he doesn't understand.
"He's very willing, he's such a nice boy and he's always smiling, always positive around everybody. He's a bit of a free spirit, but that's good! We need all kinds of characters in the team and now he's showing his commitment to us.
"I don't know how he was feeling before, we just try to produce the right amount for players and try to treat them a little bit individually for their needs, and hopefully we are in the right direction with Nico and that he can feel our total support. The only aim from us basically is to try and improve him and make him decisive for the team."