The 27-year-old netted 19 goals in all competitions last season, including a run of seven goals in seven successive games to equal the record of former Brazilian striker Bebeto.
Perez, who also scored in Deportivo's opening La Liga win over Eibar this season, will fit into Arsenal's possession based football, according to manager Arsene Wenger.
"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, Wenger told the club website.
"He's got a good eye for goal and had an outstanding season last year."
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Though no details of the deal were disclosed, British media reported that Arsenal paid around 17.1 million pounds ($22.42 million) for the striker.
Perez began his career with Atletico Madrid before spells with Rayo Vallecano, Ukrainian club Karpaty Lviv and PAOK Salonika in Greece. He sealed a permanent move to Deportivo in 2015.
Arsenal have endured a frustrating close season, snubbed by striker Jamie Vardy, who extended his contract with champions Leicester City. Olympique Lyonnais rejected their bid for forward Alexandre Lacazette.
The deal is subject to the completion of regulatory processes, the London club said.
Arsenal, who tasted their first league victory against Watford on Saturday, next host Southampton on Sept. 10.
(Reporting by Ian Rodricks in Bengaluru, editing by Ed Osmond)
