The 27-year-old has reportedly signed a long-term contract although the exact length of the deal is not known.
Perez scored 19 goals for Deportivo last season, including 17 in La Liga.
"He’s not only a goalscorer, he’s a guy who combines well with partners, who can give a final ball and makes good runs. He’s got a good eye for goal and had an outstanding season last year," Arsene Wenger said.
Arsenal have finally managed to sign a striker after seeing moves for the likes of Jamie Vardy and Alexandre Lacazette fail to materialise.