The Spanish striker was rescued by former club Deportivo La Coruna, who re-signed Perez on loan on deadline-day.
After snubbing late interest from Everton and Newcastle, Perez, 28, said: “I’m now 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 just wanted to return home.”
Perez arrived for £17m last summer but made just two Premier League starts.
He has almost certainly played his last game for Arsenal with the La Liga side eyeing a permanent move next year.
Perez added: “My future now lies here - that is my wish.”
Fellow Gunners outcast Joel Campbell followed Perez to Spain after heading back to Real Betis for another loan spell.
The Costa Rican winger, who has been farmed out six times in as many years, said: “My game is suited to the style in Spain.
“It’s important for me to be playing games.”
