The 27-year-old appeared set for a move to Everton before Arsenal rekindled an interest to capture the Spaniard
The terms of the deal were not disclosed.
"Spanish forward Lucas Perez is joining us from Deportivo La Coruna," Arsenal wrote on their official website.
Arsenal manager Arsene Wenger said: "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."
Lucas scored 19 goals in all competitions and 17 in LaLiga last season
He also netted in seven successive games.
He began his career with Atletico Madrid C and then moved to Rayo Vallecano before spells with Ukraine's Karpaty Lviv and PAOK in Greece
He joined Deportivo in 2014, initially on loan.
Lucas becomes Wenger's third summer signing - after midfielder Granit Xhaka from Borussia Monchengladbach and Rob Holding from Bolton - but more could follow, taking the Gunners' spending close to Â£100million.
Valencia's Germany defender Shkodran Mustafi is a summer-long target and a Â£30m deal is reportedly close.
Speaking last Friday, Wenger denied Lucas was a panic buy, but welcomed comparisons with Jamie Vardy, the Leicester striker the Frenchman tried and failed to lure to the Emirates Stadium earlier in the summer.
"He is a late developer, he played in a different position," Wenger said last Friday.
"He moved centrally in a successful way
I think he has good link up qualities, good finishing qualities
Let's see if we can finish the job."
When comparisons to Vardy were mentioned, Wenger said: "Yes, I like that one."
Source : PA