The Gunners landed the 28-year-old Belgium international on Friday, signing him from Brighton for an initial fee of £21million.
The move is believed to have been completed in time for Trossard to be available for Sunday's crunch visit of Manchester United.
The transfer came about after Chelsea had pipped Arsenal to the signing of Ukraine winger Mykhailo Mudryk.
But Trossard, who scored seven goals for the Seagulls this season before making the move, is already proven in the Premier League.
Asked how important that could be as his side look to win the title for the first time since 2004, Arteta replied: "Very important.
"We have to think short-term, but as well medium and long-term. He gives us all that. He's a very intelligent player.
"When you look at what he's done in the last few years, he's a player who fits our way of playing. We are happy to have him."
Trossard played under Arsenal assistant Albert Stuivenberg at Genk and Arteta said he had spoken to the Dutchman to get a glowing reference.
"We talked about everybody that is connected that we want to recruit because character is something crucial, but as well to understand how they are going to be around the club, but as well personal conversations," he added.
"Albert did (give a good reference). We are really happy to have him. He's a player we followed for a while.
"The opportunity came and we had the necessity for a player in the front line who is versatile enough to play different positions.
"He knows the league, he has enough experience here and I think he can have an immediate impact on the team."
Trossard himself now wants to play a part in delivering trophies at the Emirates Stadium.
"I'm really excited to get started," he told arsenal.com.
"This is a big club and I'm ready to show the fans what I can do. Everyone has seen how well we're doing already and I'm here to help achieve their dreams - including myself.
"I'm going to take it day by day, work hard and try to help the team to achieve their goals. (I want to) get better as well. I know the manager is a great coach and I hope to be involved in doing great things and getting better as a player in every aspect.
"I'm really excited to see the fans in the stadium. I hope I can give you my all. I want to try and create as many magic moments as possible, and hopefully we can celebrate together."