Trossard arrived at the Premier League leaders on Friday from Brighton & Hove Albion on a reported four-and-a-half-year deal for a transfer fee of £27 million.
"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 in a different position," Arteta told reporters on Friday.
"He is a player that fits our way of playing for sure, and we are happy to have him."
United are on a 10-game unbeaten run in all competitions and the only team to beat Arsenal in the Premier League so far this season, earning a 3-1 victory at Old Trafford in September.
"There were some important lessons in that game and why we lost it when in many moments we had control of the game," Arteta said.
"But we know that’s one of the qualities of United – when you have control of the game the match can get away from you because they have so much individual talent, they have good organisation and they have many ways to create problems."
Arteta said Erik ten Hag's United side have turned around things around rather fast.
"I think he has implemented a very clear way of playing. They have a really good energy around the place and a lot of things have changed in a very short period of time," he said.
Arteta added that there were no fresh injuries in the squad.
United are third in the league on 39 points after 19 games, eight points behind Arsenal who have a game in hand.