Arsenal did not disclose either the length of Perez's contract or the transfer fee, but British media reports said the 27-year-old had cost around 17 million pounds.
Arsenal are also believed to be close to signing Germany defender Shkodran Mustafi from Valencia for around 35 million pounds.
Discussing Perez, Arsenal manager Arsene Wenger told the club website: "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."
Arsenal are reported to have seen off competition from Premier League rivals Everton to secure Perez's signature.
Perez, who is uncapped, scored 19 goals for Deportivo last season, including 17 in La Liga.
He also scored the winning goal in their 2-1 win over Eibar on the opening day of this season.
He began his career with Atletico Madrid's C team and has also played for Rayo Vallecano, Ukrainian side Karpaty Lviv and Greek club PAOK.
Perez follows Swiss international midfielder Granit Xhaka, Japanese forward Takuma Asano and young English centre-back Rob Holding in arriving at Arsenal during the mid-year transfer window.
Runners-up to Leicester City last season, Arsenal are eighth in the table after three matches of the new campaign.
Original source: Arsenal seal move for Spanish striker Perez