The 28-year-old got the move he craved on deadline day, rejoining the Spanish side on loan for the remainder of the 2017-18 campaign.
Perez was restricted to 21 appearances for the Gunners, just nine of which were starts, though a number of teams – Newcastle United among them – were still keen to take him off Arsenal’s hands.
Speaking at his unveiling at the Riazor, the Spaniard said: “I’m where I want to be. I have a right to decide what is going to happen with my future and what I want to do.
“Arsenal understood that and I’m grateful to them. They understood my situation and the fact that I wanted to return home. Arsenal defended their own interests, they initially didn’t want me to return to Deportivo.
“They have reached agreements with many clubs but I clearly told them that my intention was to join Depor and no other alternative.”
Perez joined Arsenal from Deportivo last summer for a fee of £17m on the back of netting 17 goals in 37 games in the 2015-16 season.